# Khuram Ali Khan

**Khuram Ali Khan, PhD**

Associate Professor

Department of Mathematics

University of Sargodha

Sargodha - PAKISTAN.

**Email**: khuram@MathCity.org

**Field of Research:** Difference and functional equations, Real functions, Mathematical inequalities involving convex functions, Time Scales Calculus, Soft Sets

**RESEARCH MONOGRAPHS:**

- Laszlo Horváth, Khuram Ali Khan and Josip Pečarić,
*Combinatorial improvements of Jensen’s inequality/ Classical and New Refinements of Jensen’s Inequality with Applications*, Monographs in Inequalities 8, Element, Zagreb, 2014, PP. 229. ISBN: 978-953-197-594-0 (Link) - Muhammad Adil Khan, Khuram Ali Khan, Dilda Pečarić and Josip Pečarić,
*Some New Improvements of Jensen’s Inequality/ Jensen's type Inequalities in Information Theory*, Monographs in Inequalities 19, Element, Zagreb, 2020, PP. 148. ISBN: 978-953-197-679-4 (Link)

**Research Articles:**

- Khuram Ali Khan, Josip Pečarić and Ivan Perić, Differences of Weighted Mixed Symmetric Means and Related Results, J. Inequal. Appl., Vol. 2010, 16 pages, (Published on October 18, 2010), Impact Factor 0.879. (Link)
- Laszlo Horvath, Khuram Ali Khan and Josip Pečarić, Refinements of Results about Weighted Mixed Symmetric Means and Related Cauchy Means, J. Inequal. Appl., Vol. 2011, Article ID 350973, 19 pages, (Published on March 14, 2011) Impact Factor 0.73 (Link)
- Laszlo Horvath, Khuram Ali Khan and Josip Pečarić, Further Refinement of Results about Mixed Symmetric Means and Cauchy Means, Advances in Inequalities and Applications, 1 (2012), No. 1, 12-32, (Published on July 9, 2012). (Link)
- Laszlo Horvath, Khuram Ali Khan and Josip Pečarić, Refinements of Hölder and Minkowski inequalities with weights, Proc. A. Razmadze Math. Inst., vol. 158 (2012), 33-56. (Link)
- Laszlo Horvath, Khuram Ali Khan and Josip Pečarić, On Parameter Dependent Refinement of Discrete Jensen's Inequality for Operator Convex Functions, J. Math. Comput. Sci., vol. 2 (2012), No. 3, 656-672. (Link)
- Khuram Ali Khan and Josip Pečarić, Mixed Symmetric Means Related to the Classical Jensen's Inequality, Journal of Mathematical Inequalities, Vol. 7, No. 1(2013), 43–62. Impact Factor 0.718 (Link)
- Laszlo Horvath, Khuram Ali Khan and Josip Pečarić, New Refinements of Holder and Minkowski inequalities with weights, Proc. A. Razmadze Math. Inst., Vol. 161, 97-116 (2013). (Link)
- Khuram Ali Khan, C. P. Niculescu and Josip Pečarić, A Note on Popoviciu Inequality for 2D-Convex Functions, Annals of the University of Craiova, Mathematics and Computer Science Series, Vol. 40(2), 2013, 264-267 ISI.(Link)
- Laszlo Horvath, Khuram Ali Khan and Josip Pečarić, Refinement of Jensen's Inequality for Operator Convex Functions, Adv. Inequal. Appl. 2014, 2014:26. (Link)
- Qamar Din, Tarek Fawzi Abdelhamid Ibrahim, and Khuram Ali Khan, Behavior of a competitive system of second-order difference equations, The Scientific World Journal, Vol. 2014 (2014), Article ID 283982, 9 pages (Published on May 15, 2014) (Link)
- Khuram Ali Khan, Ammara Nosheen and Josip Pečarić, n-exponential Convexity of some dynamic Hardy-type functionals, Journal of Mathematical Inequalities, Vol. 8, N0. 2 (2014), 331–347 (Published in June 2014) Impact Factor 0.632. (Link)
- Qamar Din, Khuram Ali Khan, Ammara Nosheen, Stability Analysis of a System of Exponential Difference Equations, Discrete Dynamics in Nature and Society Vol. 2014 (2014), Article ID 375890, 11 pages (Published on 24 July 2014) Impact Factor 0.877. (Link)
- Khuram Ali Khan, Josip Pečarić and Ivan Perić, Generalization of Popoviciu Type Inequalities for Symmetric Means Generated by Convex Functions, J. Math. Comput. Sci., Vol 4, No 6 (2014), 1091-1113 (Published in December 2014). (Link)
- Khuram Ali Khan and Josip Pečarić, Cyclic Refinement of Beck’s Inequalities, Proc. A. Razmadze Math. Inst., Vol. 169 (2015), 83-92 (Link)
- Saad Ihsan Butt, Khuram Ali Khan and Josip Pečarić, Generalization of Popoviciu inequality for higher order convex functions via Taylor polynomial, Acta Universitatis Apulensis Seria Mathematics-Informatics, No. 42/2015 pp. 181-200 (Published June 2015) (Link)
- Laszlo Horvath, Khuram Ali Khan and Josip Pečarić, Refinement of Determinantal Inequalities of Jensen's Type, Eurasian Mathematical Journal, Vol. 6, No. 3 (2015), 30 – 44 ISI (Published September 2015).(Link)
- M. Adil Khan, G. Ali Khan, M. Jameel, Khuram Ali Khan and A. Kilicman, New refinements of Jensen-Mercer's inequality, Journal of Computational and Theoretical Nanoscience, Vol. 12, 4442–4449, 2015 (Published November 2015) IF 1.343 (Link)
- Ilko Brnetić, Khuram Ali Khan and Josip Pečarić, Refinement of Jensen's Inequality With Applications to Cyclic Mixed Symmetric Means And Cauchy Means, Journal of Mathematical Inequalities, Vol. 9, No. 4 (2015), 1309–1321 (Published in December 2015) Impact Factor 0.632 (Link)
- Saad Ihsan Butt, Khuram Ali Khan and Josip Pečarić, Popoviciu type inequalities via Green function and generalized Montgomery identity, Mathematical Inequalities and Applications, Vol. 18 No. 4 (2015), 1519–1538 (Published December 2015) Impact Factor 0.588 (Link)
- Laszlo Horvath, Khuram Ali Khan and Josip Pečarić, Cyclic refinements of the discrete and integral form of Jensen's inequality with applications, Analysis, International mathematical journal of analysis and its applications, (De Gruyter), Vol. 36 No. 4 (2016), 253-262 (Published February 2, 2016) (Link)
- Saad Ihsan Butt, Khuram Ali Khan and Josip Pečarić, Popoviciu type inequalities via Green function and Taylor polynomial, Turk. J. Math, (2016) 40(2):333-349 (Published February 10, 2016) Impact Factor 0.311 DOI: (Link)
- Laszlo Horvath, Khuram Ali Khan and Josip Pečarić, Cyclic refinements of the different versions of operator Jensen's Inequality, Electronic Journal of Linear Algebra, Vol. 31, (2016) pp. 125-133, (March, 2016) Impact Factor 0.420 DOI: (Link)
- Khuram Ali Khan, Tasadduq Niaz and Josip Pečarić, Integral form of Popoviciu inequality for convex function, Proceedings of the Pakistan Academy of Sciences, A Vol. 53 No. 3 (2016) pp. 339–348 (Published September, 2016) (HEC recognized journal; Y category). (Link)
- Saad Ihsan Butt, Khuram Ali Khan and Josip Pečarić, Popoviciu type inequalities via Hermite’s polynomial, Mathematical Inequalities and Applications, Vol. 19, No. 4 (2016), 1309–1318, Impact Factor 0.645 (2016) (Published October, 2016). (Link)
- Saad Ihsan Butt, Khuram Ali Khan and Josip Pečarić, Generalization of Popoviciu Type Inequalities via Abel-Gontscharoff Interpolating Polynomial, J. Math. Comput. Sci., Vol 7, No 2 (2017) 211-229. (Published March 1, 2017). (Link)
- Ghulam Abbas, Khuram Ali Khan, Ghulam Farid and Atiq Ur Rehman, Generalizations of some Integral Inequalities via Generalized Mittag-Leffler Function, Journal of Inequalities and Applications, (Published May 23, 2017) Impact Factor 0.630 (Link)
- Khuram Ali Khan, Muhammad Adil Khan and Uzma Sadaf, New Refinement of Jensen-Mercer's Operator inequality and applications to means, Punjab University Journal of Mathematics, Vol. 49(2) (2017), 127-151 (Published June 08, 2017). (Link)
- Ghulam Abbas, Khuram Ali Khan, Ghulam Farid and Atiq Ur Rehman, Generalized fractional integral inequalities for harmonically convex functions, Journal of Mathematical Analysis, Vol. 8(4) (2017), 1-16. ISI (Published, June 30, 2017) (Link)
- Saad Ihsan Butt, Khuram Ali Khan and Josip Pečarić, Combinatorial Improvement of Shannon Inequality and related results“ Journal of Mathematical Analysis, Vol. 8(4) (2017), Pages 97-110. ISI (Published July 31, 2017). (Link)
- Tasadduq Niaz, Khuram Ali Khan, and Josip Pečarić, On Generalization of Refinement of Jensen's Inequality using Fink's Identity and Abel-Gontcharoff Green function, Journal of Inequalities and Applications, (2017) 2017:254 (Published October 10, 2017) Impact Factor 0.966. (Link)
- Sajid Mehmood, Ghulam Farid, Khuram Ali Khan, Naveed Latif and Atiq Ur Rehman, General fractional integral inequalities for convex and m-convex functions via an extended generalized Mittag-Leffler function, Journal of inequalities and Applications, Impact Factor 1.136 (September 15, 2018). (Link)
- Naheed Ashraf, Khuram Ali Khan, Shakila Mobeen and Ammara Nosheen, Inequalities of Hardy type for Jackson Norlund integrals, Communications in Mathematics and Applications (Published , 2018) ISI. (Link)
- Tasadduq Niaz, Khuram Ali Khan, Dilda Pecaric and Josip Pecaric, Refinement of Jensen's Inequality and Estimation of f- and Renyi Divergence via Montgomery identity, Journal of inequalities and Applications IF 1.136 (Published November 19, 2018). (Link)
- Khuram Ali Khan, Tasadduq Niaz, Dilda Pecaric, Josip Pečarić, Estimation of different entropies via Abel–Gontscharoff Green functions and Fink’s identity using Jensen type functionals, Arab Journal of Mathematical Sciences, (Accepted December 18, 2018). In Press (Link)
- S. Ullah, G. Farid, Khuram Ali Khan, A. Waheed And S. Mehmood, Generalized fractional inequalities for quasi-convex functions, Advances in Difference Equations ( Published January 18, 2019) IF 1.51 (Link)
- Shahzad Ashraf, Khuram Ali Khan and Ammara Nosheen, Hardy-Copson type inequalities on time scales for the functions of “n” independent variables, International Journal of Analysis and Applications, Vol. 17, No. 2 (2019), 244-259 ISI (Published March 01, 2019). (Link)
- Ghulam Farid, Khuram Ali Khan, Atiq ur Rehman, Farooq Ahmed Shah, Asif Waheed and Sajid Mehmood, On Caputo k -fractional derivatives and associated inequalities, IEEE Access, Vol. 7, 32137-32145 (Published March 12, 2019), IF: 4.098 (Link)
- Masud Ahmad, Khalid Mahmood Awan, Shehzad Hameed, Khuram Ali Khan, Ammara Nosheen, Bivariate Montgomery identity for alpha diamond integrals, Advances in Difference Equations (Published August 02, 2019). IF 1.51 (Link)
- Shakila Mobeen, Naheed Ashraf, Ammara Nosheen and Khuram Ali Khan, Weighted Cebysev type inequalities for double integrals on time scale, Journal of inequalities and special functions Vol. 10 No. 02 (2019), 61-77 (Published March 19, 2019) ISI. (Link)
- Waseem Ahmad, Khuram Ali Khan, Ammara Nosheen and Maroof Ahmad Sultan Ammara Nosheen, Copson, Leindler type inequalities for function of several variables on Time Scales, Punjab University Journal of Mathematics (Published July 11, 2019) ISI. (Link)
- Muhammad Adeel, Khuram Ali Khan, Dilda Pečarić and Josip Pečarić, Generalization of Levinson inequality with application to information theory, Journal of Inequalities and Applications, Article No. 230 (2019) (Published August 29, 2019). IF 1.136 (Link)
- Khuram Ali Khan, Tasadduq Niaz, Dilda Pecaric, Josip Pečarić, Estimation of Different Entropies via Taylor One Point and Taylor Two Points Interpolations using Jensen Type Functionals, International Journal of Analysis and Applications, Vol. 17, No. 5 (2019), 686-710 ISI (Published September 02, 2019). (Link)
- Muhammad Adeel, Khuram Ali Khan, Dilda Pečarić and Josip Pečarić, Levinson type inequalities for higher order convex functions via Abel-Gontscharoff interpolation, Advances in Difference Equations, (2019) 2019:430 (Published October 11, 2019). IF 1.51 (Link)
- Ammara Nosheen, Aneela Nawaz, Khuram Ali Khan, and Khalid Mehmood Awan, Multivariate Hardy and Littlewood Inequalities on Time Scales, Arab Journal of Mathematical Sciences (online on December 28, 2019). (Link)
- Muhammad Adeel, Khuram Ali Khan, Dilda Pečarić and Josip Pečarić, Estimation of f-divergence and Shannon entropy by Levinson type inequalities via new Green functions and Lidstone polynomial, Advances in Difference Equations, (Published January 14, 2020). IF 1.51 (Link)
- Khuram Ali Khan, Tasadduq Niaz, Dilda Pečarić, Josip Pečarić, Estimation of different entropies via Lidstone polynomial using Jensen type functionals, Arabian Journal of Mathematics, ISI (Published February 18, 2020). (Link)
- Iqrar Ansari, Khuram Ali Khan, Ammara Nosheen, Dilda Pečarić and Josip Pečarić, Shannon Type Inequalities via Time Scales Theory, Advances in Difference Equations (Published March 20, 2020). IF 1.51 (Link)
- Sajid Mehmood, Ghulam Farid, Khuram Ali Khan, Muhammad Yussouf, New Hadamard and Fejér-Hadamard fractional inequalities for exponentially m-convex function, Engineering and Applied Science Letter, Vol. 3 (2020), No. 1, pp. 45 – 55. (Published March 20, 2020) (Link)
- 49. Sajid Mehmood, Ghulam Farid, Khuram Ali Khan, Muhammad Yussouf, New fractional Hadamard and Fejér-Hadamard inequalities associated with exponentially (h, m) convex functions, Engineering and Applied Science Letter, Vol. 3 (2020), No. 2, 9-18. (Published April 09, 2020) (Link)
- Muhammad Adeel, Khuram Ali Khan, Dilda Pečarić and Josip Pečarić, Estimation of f-divergence and Shannon entropy by using Levinson type Inequalities for higher order convex functions via Hermite interpolating polynomial, Journal of Inequalities and Applications, (Published May 12, 2019). IF 1.136 (Link)
- Muhammad Adeel, Khuram Ali Khan, Dilda Pečarić and Josip Pečarić, Estimation of f-divergence and Shannon entropy by Levinson type inequalities for higher-order convex functions via Taylor polynomial, Journal of Mathematics and Computer Science, Vol. 21, Issue 4, 322—334, (2020). (Published May 15, 2020). ISI (Link)
- Tasadduq Niaz, Khuram Ali Khan, and Josip Pečarić, On Refinement of Jensen’s Inequality for 3-convex function at a point, Turkish J. Ineq., 4 (1) (2020), Pages 70-80. (Published June 11, 2020). (Link)
- Khuram Ali Khan, Tasadduq Niaz, Dilda Pečarić, Josip Pečarić, Estimation of different entropies via Hermite interpolating polynomial using Jensen type functionals, The Journal of Analysis, ISI (Published June 12, 2020). (Link)
- Khuram Ali Khan, Khalid Mahmood Awan, Sumaiya Malik, Ammara Nosheen, Extension of Montgomery identity via Taylor polynomial on time scales, Turkish Journal of Mathematics (Online on June 22, 2020). IF 0.658 (Link)
- Muhammad Adeel, Khuram Ali Khan, Dilda Pečarić and Josip Pečarić, Levinson-type Inequalities via new Green functions and Montgomery identity, Open Mathematics Vol. 18 No.1 (Published July 01, 2020) ISSN: 2391-5455. IF 0.773 (Link)
- Xiaoli Qiang, Ghulam Farid, Muhammad Yussouf, Khuram Ali Khan, Atiq U Rehman, New Generalized Fractional Versions of Hadamard And Fejer Inequalities for Harmonically Convex Functions, Journal of Inequalities and Applications 2020:191 IF 1.47 (Published July 17, 2020). (Link)
- Nouman Siddique, Muhammad Imran, Khuram Ali Khan and Josip Pečarić, Majorization inequalities via Green functions and Fink’s identity with applications to Shannon entropy, Journal of Inequalities and Applications 2020:192 IF 1.47 (Published July 22, 2020). (Link)
- Nouman Siddique, Muhammad Imran, Khuram Ali Khan and Josip Pečarić, Difference equations related to majorization theorems via Montgomery identity and Green’s functions with application to the Shannon entropy, Advances in Difference Equations 2020:430 IF 2.42 (Published August 18, 2020). (Link)
- Muhammad Adil Khan, Shahid Khan, Inam Ullah, Khuram Ali Khan and Yuming Chu, A novel approach to the Jensen gap through Taylor's theorem, Mathematical Methods in the Applied Sciences (Published October 14, 2020). IF 1.626 (Link)
- Hafiz Abdul Moeed, Daoowd Ahmed, Ammara Nosheen, Khuram Ali Khan, Hardy type Inequalities for Superquadratic Functions via Jackson Norlund Integrals, Journal of Mathematics and Computer Science (Published November 01, 2020). ISI (Link)
- Iqrar Ansari, Khuram Ali Khan, Ammara Nosheen, Dilda Pečarić and Josip Pečarić, Some inequalities for Csiszar divergence via theory of time scales, Advances in Difference Equations (2020) 2020:698. (Published December 10, 2020). IF 2.421 (Link)
- Hafiz Abdul Moeed, Daoowd Ahmed, Ammara Nosheen, Khuram Ali Khan, Hardy type Inequalities for Super quadratic Functions via Jackson Norlund Integrals, Journal of Mathematics and Computer Science 23 (3) 203–212 2021 (Published online November 01, 2020) (Link)
- Ghulam Farid, Muhammad Yussouf, Khuram Ali Khan and Chahn Yong Jung, Hadamard and Fejer-Hadamard Inequalities for Further Generalized Fractional Integrals Involving Mittag-Leffler Functions, Journal of Mathematics IF 0.971 (Published March 16, 2021). (Link)
- Muhammad Adeel, Khuram Ali Khan, Dilda Pečarić and Josip Pečarić, Estimation of f-divergence and Shannon entropy by Levinson type inequalities via Lidstone interpolating polynomial, Transactions of A. Razmadze Mathematical Institute, Vol. 175 (1) 1-11 (Published April, 2021). (Link)
- Daoowd Ahmed, Khuram Ali Khan and Ammara Nosheen, Inequalities of Hardy-type for Multiple Integrals on Time Scales, Journal of Prime Research in Mathematics, Vol. 17 (2021), Issue 1, pp. 21 – 34 (Published May 18, 2021) HEC Recognized Y category. (Link)
- Ammara Nosheen, Aneeqa Aslam, Khuram Ali Khan, Khalid Mehmood Awan, Hamid Reza Morad, Multivariate Dynamic Sneak-Out Inequalities on Time Scales, Journal of Mathematics, Volume 2021 Article ID 9978050 IF 0.971 (Published May 27, 2021) (Link)
- Usama Hanif, Ammara Nosheen, Rabia Bibi, Khuram Ali Khan, Hamid Reza Moradi, Some Hardy-Type Inequalities for Superquadratic Functions via Delta Fractional Integrals, Mathematical Problems in Engineering Volume 2021 Article ID 9939468 (Published May 28, 2021) IF 1.43 (Link)
- Iqrar Ansari, Khuram Ali Khan, Ammara Nosheen, Dilda Pečarić and Josip Pečarić, Estimation of divergence measures via weighted Jensen inequality on time scales, Journal of Inequalities and Applications 2021, 93 (2021) ISSN 1029-242X (Published May 28, 2021). IF 2.021 (Link)
- Sarfraz Ali, Sabir Iqbal, Khuram Ali Khan, Hamid Reza Moradi, Amended FRW Metric and Reyni Dark Energy Model, Advances in High Energy Physics Volume 2021, Article ID 9704909, 9 pages 9704909 (Published June 16, 2021) IF 1.771 (Link)
- Iqrar Ansari, Khuram Ali Khan, Ammara Nosheen, Dilda Pečarić and Josip Pečarić, Estimation of divergence measures on time scales via Taylor’s polynomial and Green’s function with applications in q-calculus, Advances in Difference Equations (2021) 2021:374. (Published August 10, 2021). IF 3.761 (Link)
- Wenyan Jia, Muhammad Yussouf, Ghulam Farid, Khuram Ali Khan, Hadamard and Fejér–Hadamard Inequalities for -Convex Functions via Riemann–Liouville Fractional Integrals, Mathematical Problems in Engineering vol. 2021, Article ID 9945114, 12 pages, 2021 (published August 16, 2021). IF 1.43 (Link)
- Iqrar Ansari, Khuram Ali Khan, Ammara Nosheen, Dilda Pečarić and Josip Pečarić, Estimation of Divergences on time scales via Green function and Fink’s Identity, Advances in Difference Equations 2021, Article number: 394 (2021) (Published August 24, 2021). IF 3.761 (Link)
- Muhammad Adeel, Khuram Ali Khan, Dilda Pečarić and Josip Pečarić, Entropy results for Levinson-type inequalities via Green functions and Hermite interpolating polynomial, Aequationes Mathematicae, (2021) (Published August 25, 2021). IF 0.984 (Link)
- Saad Ihsan Butt, Muhammad Umar, Khuram Ali Khan, Artion Kashuri and Homan Emadifar, Fractional Hermite–Jensen–Mercer Integral Inequalities with respect to another Function and Application, Complexity, 2021 Article ID 9260828 (Published September 06, 2021). IF 2.121 (Link)
- Saad Ihsan Butt, Saba Yousaf, Atifa Asghar, Khuram Ali Khan, Hamid Reza Moradi, New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function, Journal of Function Spaces, Vol. 2021, Article ID 5868326, 11 page (Published October 25, 2021). IF 1.281 (Link)
- Sarfraz Ali, Muhammad Hammad Waheed, Muhammad Imran Asjad, Khuram Ali Khan, Thanin Sitthiwirattham and Chanon Promsakon, The Sharma–Mittal Model’s Implications on FRW Universe in Chern–Simons Gravity, Universe 2021, 7, 428. (Published November 10, 2021) IF 2.813 (Link)
- Muhammad Bilal, Khuram Ali Khan, Hijaz Ahmad, Ammara Nosheen, Khalid Mahmood Awan, Sameh Askar, Mosleh Alharthi, Some Dynamic Inequalities via Diamond Integrals for Function of Several Variables, Fractal and Fractional 2021, 5, 207 (Published November 11, 2021). IF 3.577 (Link)
- Allah Ditta, Khuram Ali Khan, Khalid Mahmood Awan, Ammara Nosheen, Hamid Reza Moradi, Extensions of Ostrowski type inequalities via h-integrals and s-convexity, Journal of Mathematics Vol. 2021, Article ID 2416819, 10 pages (Published November 11, 2021). IF 0.971 (Link)
- Iqrar Ansari, Khuram Ali Khan, Ammara Nosheen, Dilda Pečarić and Josip Pečarić, New entropic bounds on time scales via Hermite interpolating polynomial, Journal of Inequalities and Applications 2021, Article number: 195 (2021) ISSN 1029-242X (Published December 11, 2021). IF 2.021 (Link)
- Fuzhang Wang, Usama Hanif, Ammara Nosheen, Khuram Ali Khan, Hijaz Ahmad and Kamsing Nonlaopon, Some Hardy-type Inequalities for Convex Functions via Delta Fractional Integrals, FRACTALS Vol. 30, No. 1 (2022) 2240004 (15 pages) ISSN (online): 1793-6543 (Published September 08, 2021). IF 4.555 (Link)
- Khuram Ali Khan, Allah Ditta, Ammara Nosheen, Khalid Mahmood Awan, Rostin Matendo Mabela, Ostrowski type inequalities for s-convex functions via q-integrals, Journal of Function Spaces, Vol. 2022, Article ID 8063803, 8 pages. (Published January 20, 2022). IF 1.281 (Link)
- Sumaiya Malik, Khuram Ali Khan, Ammara Nosheen, Khalid Mahmood Awan, Generalization of Montgomery identity via Taylor formula on time scales, Journal of Inequalities and Applications (2022) 2022:24 ISSN 1029-242X (Published February 14, 2022). IF 2.021 (Link)
- Jamshed Nasir, Shahid Qaisar, Saad Ihsan Butt, Khuram Ali Khan, Rostin Matendo Mabela, Some Simpson’s Riemann–Liouville Fractional Integral Inequalities with Applications to Special Functions, Journal of Function Spaces Vol. 2022, Article ID 2113742, 12 pages (Published February 23, 2022) ISSN: 2314-8888. IF 1.281 (Link)
- Muhammad Adeel, Khuram Ali Khan, Dilda Pečarić and Josip Pečarić, Estimation of f-divergence and Shannon entropy by Levinson type inequalities via Fink’s identity, FILOMAT, 36:2 (2022), 527–538 (Published March 01, 2022). IF 0.988 (Link)
- Saad Ihsan Butt, Saba Yousaf, Khuram Ali Khan, Rostin Matendo Mabela, Abdullah M. Alsharif, Fejer-Pachpatte-Mercer-Type Inequalities for Harmonically Convex Functions Involving Exponential Function in Kernel, Mathematical Problems in Engineering Vol. 2022, Article ID 7269033, 19 pages (Published March 02, 2022) ISSN: 1563-5147. IF 1.43 (Link)
- Atiqe Ur Rahman, Muhammad Saeed, Khuram Ali Khan, Rostin Matendo Mabela, Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set Inclusion, Journal of Function Spaces Vol. 2022, Article ID 6998104, 10 pages (Published March 09, 2022) ISSN: 1563-5147. IF 1.281 (Link)
- Atiqe Ur Rahman, Muhammad Saeed, Khuram Ali Khan, Ammara Nosheen, Rostin Matendo Mabela, An Algebraic Approach to Modular Inequalities Based on Interval-Valued Fuzzy Hypersoft Sets via Hypersoft Set-Inclusions, Journal of Function Spaces Vol. 2022, Article ID 1384541, 15 pages (Published May 10, 2022) ISSN: 1563-5147. IF 1.281 (Link)
- Iqrar Ansari, Khuram Ali Khan, Ammara Nosheen, Dilda Pečarić and Josip Pečarić, Estimation of entropies on time scales by Lidstone's interpolation using Csiszár-type functional, Hacettepe J. Math Stat. Vol. 51 (3), 817 - 833 ISSN: 2651-477X (Published June 01, 2022). IF 0.867 (Link)
- Saad Ihsan Butt, Ammara Nosheen, Jamshed Nasir, Khuram Ali Khan, Rostin Matendo Mabela, New Fractional Mercer-Ostrowski Type Inequalities with respect to Monotone Function, Mathematical Problems in Engineering Vol. 2022, Article ID 7067543, 14 pages (Published May 18, 2022) ISSN: 1563-5147. IF 1.43 (Link)
- Atiqe Ur Rahman, Khuram Ali Khan, Ammara Nosheen, Muhammad Saeed, Thongchai Botmart, Nehad Ali Shah, Weighted Ostrowski type inequalities via Montgomery identity involving double integrals on time scales, AIMS Mathematics Vol. 7(9): 16657–16672 (Published July 12, 2022) ISSN 2473-6988. IF 2.739 (Link)
- Sarfraz Ali, Maryam Saif, Khuram Ali Khan, Nehad Ali Shah, Wajaree Weera, A Note on Varying G and L in Chern–Simons Modified Gravity, Symmetry 2022, 14(7), 1430. (Published July 12, 2022) IF 2.940. (Link)
- Saad Ihsan Butt, Saima Rashid, Iram Javed, Khuram Ali Khan, Rostin Matendo Mabela, New Fractional Estimates of Simpson-Mercer Type for Twice Differentiable Mappings Pertaining to Mittag-Leffler Kernel, Journal of Function Spaces Vol. 2022, Article ID 4842344, 14 pages (Published September 05, 2022) ISSN: 1563-5147. IF 1.281 (Link)
- Xiaoming Wang, Khuram Ali Khan, Allah Ditta, Ammara Nosheen, Khalid Mahmood Awan, Rostin Matendo Mabela, New Developments on Ostrowski Type Inequalities via q-Fractional Integrals Involving s-Convex Functions, Journal of Function Spaces, Vol. 2022, Article ID 9742133, 12 pages (Published October 13, 2022). IF 1.281 (Link)
- Khuram Ali Khan, Shaista Ayaz, Imdat Iscan, Nehad Ali Shah, Wajaree Weera, Extensions of Holder-Iscan inequality via n-times Differentiable (s,m)–convex Functions, AIMS Mathematics 2023, Vo. 8(1): 1620-1635. (Published October 24, 2022) IF 2.739 (Link)
- Ammara Nosheen, Anum Saba, Khuram Ali Khan, Michael Kikomba Kahungu, q,h-Opial-Type Inequalities via Hahn Operators, Discrete Dynamics in Nature and Society Vol. 2022 Article ID 2650126 (Published October 26, 2022) ISSN: 1607-887X (Online) IF 1.457 (Link)
- Muhammad Bilal, Khuram Ali Khan, Ammara Nosheen, Josip Pečarić, Generalizations of Shannon type inequalities via diamond integrals on time scales, Journal of Inequalities and Applications 2023, 24 (2023). IF 2.021 ISSN 1029-242X Published (February 10, 2023) (Link)
- Ammara Nosheen, Maria Tariq, Khuram Ali Khan, Nehad Ali Shah, Jae Dong Chung, On Caputo Fractional Derivatives and Caputo–Fabrizio Integral Operators via (s,m)-Convex Functions, Fractal Fractional 2023, 7, 187 (Published February 13, 2023) IF 1.457 (Link)
- Muhammad Ihsan, Muhammad Saeed, Khuram Ali Khan, Ammara Nosheen, An algebraic approach to the variants of convexity for soft expert approximate function with intuitionistic fuzzy setting, Journal of Taibah University for Science Vol. 17(1) 2182144 (Published February 27, 2023) ISSN 1658-3655. IF 3.459 (Link)
- Muhammad Bilal, Khuram Ali Khan, Ammara Nosheen, Josip Pečarić, Estimation of divergence measures for Diamond Integrals via Greens function and Taylor’s polynomial, Research in Mathematics 2023, 10(1), 2179450. (Y category on HJRS) ISSN 2768-4830 (Published March 06, 2023) (Link)
- Muhammad Bilal, Khuram Ali Khan, Ammara Nosheen, Josip Pečarić, Generalization of Some Inequalities Containing Entropies on Time Scales, Qualitative Theory of Dynamical Systems (2023) 22:71. IF 0.931 ISSN 1662-3592 (Published March 17, 2023) (Link)
- Muhammad Arshad, Muhammad Saeed, Khuram Ali Khan, Nehad Ali Shah, Wajaree Weera, Jae Dong Chung, A robust MADM-approach to recruitment-based pattern recognition by using similarity measures of interval-valued fuzzy hypersoft set, AIMS Mathematics 2023 8(5): 12321–12341. IF 2.739 ISSN 2473-6988 (Published March 24, 2023 (Link)
- Ammara Nosheen, Khalid Mahmood Awan, Khuram Ali Khan, Hijaz Ahmad, Atia Tul Qadeer, Hardy-Leindler Type Inequalities For Multiple Integrals on Time Scales, Mathematica Slovaca 2023 73(2), 353-368. (Published March 31, 2023) IF 0.996 ISSN 0139 – 9918 (Link)
- Muhammad Bilal, Khuram Ali Khan, Ammara Nosheen, Josip Pečarić, Generalization of Some Inequalities Containing Entropies on Time Scales, Journal of Inequalities and Applications 2023, 55 (2023), (Published April 14, 2023) IF 2.021 ISSN 1029-242X (Link)
- Ammara Nosheen, Sana Ijaz, Khuram Ali Khan*, Khalid M. Awan, Marwan Albahar, Mohammad Thanoon, Some New q-Symmetric Integral Inequalities Involving s-Convex Functions, Symmetry 2023, 15(6), 1169 (Published May 29, 2023) IF 2.940 EISSN 2073-8994 (Link)
- Ammara Nosheen, Sadaf Nawaz, Khuram Ali Khan, Rostin Matendo Mabela, Interval Valued Jensen’s Inequalities for h-Convex Functions on Time Scales, Arab Journal of Basic and Applied Sciences 2023, Vol. 30, No. 1, 341–353 (Published May 31, 2023) ISSN: 2576-5299 (HJRS; X category) (Link)
- Khuram Ali Khan*, Ammara Nosheen, Sumaiya Malik, Muhammad Kashif, Rostin Matendo Mabela, Generalizations of Steffensen’s Inequality for Higher Order Convex Functions Involving an Extension of Montgomery Identity on Time Scale, Inverse Problems in Science and Engineering 2023, Vol. 31, No. 1, 2214300 (Published June 11, 2023) ISSN: 2769-0911 IF 1.440 (Link)
- Ali Asghar, Khuram Ali Khan, Marwan Ali Albahar, Abdullah Alammari, An optimized multi-attribute decision-making approach to construction supply chain management by using complex picture fuzzy soft set, PeerJ Computer Science 2023, 9:e1540 (Published August 30, 2023) eISSN: 2376-5992 IF 3.8 (Link)

## PhD Supervision

- KHALID MAHMOOD AWAN, On the Stefensen's generalization of Chebyshev functional with applications; Department of Mathematics, University of Sargodha. (February 16, 2018)
- GHULAM ABBAS, Hermite-Hadamard-Fejér type integral inequalities via generalized fractional integral operators; Department of Mathematics, University of Sargodha (May 03, 2019).
- TASADUQ NIAZ, New Generalizations of Jensen-Type Inequalities via Interpolating Polynomials; Department of Mathematics, University of Sargodha (July 09, 2020).
- MUHAMMAD ADEEL, Levinson-type Inequalities via Interpolating Polynomials; Department of Mathematics, University of Sargodha (November 05, 2020).
- Muhammad Yussouf, Hadamard and Fejer type Inequalities via Fractional Integral Operators for Extended Generalized Mittag-Leffler Function, Department of Mathematics, University of Sargodha (April 15, 2021).
- NOUMAN SIDDIQUE, Majorization Type Inequalities via Interpolating Polynomials, Department of Mathematics, GC University Faisalabad (July 02, 2021).
- IQRAR ANSARI, Inequalities Involving Different Types of Entropies via Time Scale Calculus; Department of Mathematics, University of Sargodha (February 23, 2022).
- SUMYYA MALIK, Generalized Montgomery identity via Time Scale Calculus; Department of Mathematics, University of Sargodha. (May 16, 2023).
- Muhammad Bilal, Entropies and Divergence Measures via Diamond integrals on Time Scales; Department of Mathematics, University of Sargodha. (Thesis Submitted on May 24, 2023)

# MPhil Supervision

- SUMBUL, Qualitative behavior of discrete Lotka- Volterra type model; Department of Mathematics, University of Sargodha, February 2014.
- RANA MUHAMMAD JAHANGEER, Inequalities via theory of time scale; Department of Mathematics, University of Sargodha, October 2014.
- SOBIA NAWAZ, Qualitative Properties of Rational Difference Equations; Department of Mathematics, University of Sargodha, October 2014.
- RUQAYYA HAFEEZ, Global Behaviour of Non Linear Difference Equations; Department of Mathematics, University of Sargodha, October 2014.
- TANVEER AHMED, Hölder and Minkowski inequalities for function of several variables; Department of Mathematics, University of Sargodha, August 2015.
- UZMA SADAF, Refinement of Jensen’s Operator’s inequality; Department of Mathematics, University of Sargodha, September 2015.
- NASIRA KAUSAR, Dynamic inequalities of Hardy type via time scales; Department of Mathematics, University of Sargodha, February 2016.
- SUMAIYA MALIK, Analytic behaviour of plant-herbivore and discrete predator-prey models; Department of Mathematics, University of Sargodha, September 2016.
- MADIHA, Infectious disease model by incidence rates; Department of Mathematics, University of Sargodha, February 2017.
- IKRAM ULLAH, Classical inequalities for diamond alpha integrals on time scales; Department of Mathematics, University of Sargodha (Mandi Bahau Din Campus), May 2017.
- ISHRAT FATIMA, Jessen's Inequality for Isotonic Linear Functionals via Time Scales, Department of Mathematics, University of Sargodha, October 2017.
- M. RASHID MAJID, Integral Analogue of Popoviciu's Inequality, Department of Mathematics, University of Sargodha (Lyallpur Campus Faisalabad), October 2017.
- SANA GUL, Analytical Solution of Susceptible Infected Recovered (SIR) model by using Homotopy Analysis Method (HAM), Department of Mathematics, University of Sargodha (Lyallpur Campus Faisalabad), January 2018.
- MEHAK MUSHTAQ, Some Applications of Hamy Symmetric Functions, Department of Mathematics, University of Sargodha, March 2018.
- ALIA RAMZAN, Dynamic Opial inequalities on time scales, Department of Mathematics, University of Sargodha, January 15, 2019.
- BISMA KAZMI, Ostrowski and Hausdroff Type Inequalities via Time Scale Calculus, Department of Mathematics, University of Sargodha, February 18, 2019.
- SADAF BASHIR, Mixed Symmetric Means related to new Refinements of Discrete Holder's Inequality, Department of Mathematics, University of Sargodha, February 18, 2019.
- TAHREEM ABBAS, Hardy-Hilbert Type Inequalities via Diamond Integrals, Department of Mathematics, University of Sargodha, December 17, 2019.
- ALI ASGHAR, Some Hardy-Type Inequalities via Diamond-Alpha Integrals, Department of Mathematics, University of Sargodha, December 17, 2019.
- NADIA SAIF, Sharp Inequalities involving Euler’s Gamma Function; Department of Mathematics, University of Sargodha (Ex-PPP Women Campus Faisalabad), December 17, 2019.
- AYESHA TARIQ, Hilbert type Inequalities for Multiple Integrals; Department of Mathematics, University of Sargodha (Ex-PPP Women Campus Faisalabad), December 17, 2019.
- SONIA MARIUM, Some Extensions of Cauchy Schwarz Inequality; Department of Mathematics, University of Sargodha (Ex-PPP Women Campus Faisalabad), December 17, 2019.
- Rizwana Afzal, Jensen’s inequality with applications to means for cyclic data; Department of Mathematics, University of Sargodha (Ex-PPP Women Campus Faisalabad), June 11, 2020.
- Awais Rasheed, Inequalities on time scales via interpolating polynomials; Department of Mathematics, University of Sargodha, September 02, 2020.
- Muhammad Bilal, Hardy type inequalities for multiple integrals via theory of time scales, Department of Mathematics, University of Sargodha, September 02, 2020.
- Allah Ditta, Ostrowski Type Inequalities for s-Convex Functions in Second Sense via q-Fractional Integrals, Department of Mathematics, University of Sargodha, July 09, 2021.
- Ehsan Zakaullah, inequalities, Some Dynamic Hardy-type Inequalities via Fractional Integrals, Department of Mathematics, University of Sargodha, August 30, 2021.
- Asima Iqbal, A Parameter Dependent Refinement of Holder's and Minkowski's Inequalities, Department of Mathematics, University of Sargodha September 24, 2021).
- Shaista Ayaz, Inequalities for n-times Differentiable Functions via Different Types of Convexities, Department of Mathematics, University of Sargodha. (2022)
- Majid Khan, Hermite-Hadamard Type Inequalities for Quasi-Convex Functions via q-Calculus, Department of Mathematics, University of Sargodha. (August 12, 2022)
- Saeeda Fatima, Hermite-Hadamard Type Fractional Integral Inequalities for s-Convex and (s,m)-Convex Functions, Department of Mathematics, University of Sargodha. (November 11, 2022)
- Sonia Afzal, Inequalities Involving Generalized Strongly n-Polynomial Exponential Type p-Convex Functions of Higher Order, Department of Mathematics, University of Sargodha. (November 11, 2022)
- Hameed Ullah, Estimations of Some Entropies for Higher Order Convex Functions, Department of Mathematics, University of Sargodha. (November 14, 2022)

# PHD STUDENTS IN PROGRESS

- Awais Rasheed, Generalizations of Inequalities for 3-Convex Functions via Green Functions; Department of Mathematics, University of Sargodha. (Synopsis approved June 06, 2022)
- Ali Asghar, New Developments of Complex Soft Set-Like Models; Department of Mathematics, University of Sargodha. (Synopsis approved June 06, 2022)
- Muhammad Sajid, About Hypersoft Sets, Department of Mathematics, University of Sargodha.

# MPHIL STUDENTS IN PROGRESS

- Muhammad Ramzan, Trapezium Type Inequalities for Some Classes of Convex Functions, Department of Mathematics, University of Sargodha.
- Moheeb Khalid, Popuviciu Type Inequalities via interpolations, Department of Mathematics, University of Sargodha.
- Muhammad Rizwan, Inequalities involving Delta Diamond Integrals, Department of Mathematics, University of Sargodha.
- Ahmed Sher, Inequalities on Soft Sets, Department of Mathematics, University of Sargodha.
- Rimsha Hameed, Time Scale Inequalities for Different Integrals, Department of Mathematics, University of Sargodha.

# PHD THESIS REVEIEWED

- RISHI NAEEM, On Jensen’s Inequality and Related Results; Department of Mathematics, School of Naturel Sciences, NUST Islamabad, October 24, 2019.
- NAILA MEHREEN, Generalized convex functions with some integral properties; Department of Mathematics, School of Naturel Sciences, NUST Islamabad, January 27, 2020.
- RUBY NASIR, Computing Edge Version of Metric Dimension and Edge Version of Doubly Resolving Sets of the Families of Graphs; University of Management and Technology School of Science, Department of Mathematics, July, 2022.
- MUHAMMAD NAVEED JAFAR, Development of Techniques to Solve Multi-Objective, Multi-Attributes with Disjoint Attributive Value Problems in Neutrosophic Hypersoft Set Environment; University of Management and Technology School of Science, Department of Mathematics, July, 2022.
- ABDUL MALIK SULTAN, Dynamic Properties of Some Cosmological Systems, COMSATS University Islamabad, Lahore Campus, July 06, 2023.

# M.PHIL THESIS EVALUATOR

- GC University Faisalabad
- University of Peshawar
- University of Malakand
- University of Karachi
- IBA, Karachi
- University of Okara
- Federal Urdu University of Arts, Science & Technology, Karachi/Islamabad
- The University of Lahore
- COMSATS University Islamabad
- University of Management and technology, Lahore
- University of Swat

# MSC/BS PROJECT EVALUATOR

- COMSATS University Islamabad (Lahore, Sahiwal, Attock Campus)

# BS MATH PROJECTS SUPERVISED

- RAHEELA KANWAL, New Integral Results on Holder type Inequalities, Department of Mathematics, University of Sargodha, August 2020.
- AYESHA SARFRAZ, Recent Development of Some Holder's type Inequalities, Department of Mathematics, University of Sargodha, August 2020.
- MARIAM AKBER, The Hermite Hadamard Inequality and Bounds for some Special Means, Department of Mathematics, University of Sargodha, August 2020.
- MUHAMMAD ASIF, Trigonometric inequalities, Department of Mathematics, University of Sargodha, June 2018.
- MAHEEN SARWER, Inequalities involving hyperbolic trignometric functions, Department of Mathematics, University of Sargodha, May 2018.
- SAMRA AHMED, Inequalities involving Pade approximation, Department of Mathematics, University of Sargodha, May 2018.
- KINZA ALI NAWAZ, Descriptive review of cyclic mixed symmetric means and Cauchy means, Department of Mathematics, University of Sargodha, August 2017.
- M. JABIR KHAN, Upper and lower semicontinuity; Department of Mathematics, University of Sargodha, August 2015.
- IRAM AYUB, A descriptive review of difference equations; Department of Mathematics, University of Sargodha, August 2014.

# SIGNIFICANCE

- Superintendent, Iqbal Hall (Boys Hostel), UNIVERSITY OF SARGODHA
- HEC approved supervisor
- Reviewer for MATHEMATICAL REVIEWS/MATHSCINET REVIEWER NUMBER: 105832
- MEMBER OF AMERICAN MATHEMATICAL SOCIETY
- MEMBER OF INTERNATIONAL SOCIETY OF DIFFERENCE EQUATIONS
- MEMBER OF PAKISTAN MATHEMATICAL SOCIETY
- MODERATOR AT http://www.mathcity.org
- Editor, Transactions in Mathematical and Computational Sciences

## Currently Teaching Courses

- Real Analysis
- Orthogonal Polynomials

## Courses Taught (Undergraduate Level)

- Real Analysis
- Measure Theory
- Functional Analysis

## Courses Taught (Postgraduate Level)

- Fractional Calculus
- Time Scales Calculus
- Applications of inequalities
- Inequalities involving convex functions
- Convex Analysis