Khuram Ali Khan


Khuram Ali Khan, PhD
Assistant 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

RESEARCH MONOGRAPHS:

  1. 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)
  2. 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:

  1. 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)
  2. 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)
  3. 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)
  4. 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)
  5. 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)
  6. 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)
  7. 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)
  8. 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)
  9. Laszlo Horvath, Khuram Ali Khan and Josip Pečarić, Refinement of Jensen's Inequality for Operator Convex Functions, Adv. Inequal. Appl. 2014, 2014:26. (Link)
  10. 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)
  11. 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)
  12. 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)
  13. 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)
  14. Khuram Ali Khan and Josip Pečarić, Cyclic Refinement of Beck’s Inequalities, Proc. A. Razmadze Math. Inst., Vol. 169 (2015), 83-92 (Link)
  15. 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)
  16. 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)
  17. 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)
  18. 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)
  19. 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)
  20. 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)
  21. 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)
  22. 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)
  23. 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)
  24. 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)
  25. 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)
  26. 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)
  27. 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)
  28. 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)
  29. 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)
  30. 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)
  31. 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)
  32. 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)
  33. 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)
  34. 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)
  35. 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)
  36. 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)
  37. 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)
  38. 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)
  39. 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)
  40. 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)
  41. 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)
  42. 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)
  43. 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)
  44. 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)
  45. 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)
  46. 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)
  47. 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)
  48. 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. 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)
  50. 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)
  51. 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)
  52. 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)
  53. 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)
  54. 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)
  55. 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)
  56. 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)
  57. 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)
  58. 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)
  59. 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)
  60. 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)
  61. 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)

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PhD Supervision

  1. KHALID MAHMOOD AWAN, On the Stefensen's generalization of Chebyshev functional with applications; Department of Mathematics, University of Sargodha. (February 16, 2018)
  2. GHULAM ABBAS, Hermite-Hadamard-Fejér type integral inequalities via generalized fractional integral operators; Department of Mathematics, University of Sargodha (May 03, 2019).
  3. TASADUQ NIAZ, New Generalizations of Jensen-Type Inequalities via Interpolating Polynomials; Department of Mathematics, University of Sargodha (July 09, 2020).
  4. MUHAMMAD ADEEL, Levinson-type Inequalities via Interpolating Polynomials; Department of Mathematics, University of Sargodha (November 05, 2020).

MPhil Supervision

  1. SUMBUL, Qualitative behavior of discrete Lotka- Volterra type model; Department of Mathematics, University of Sargodha, February 2014.
  2. RANA MUHAMMAD JAHANGEER, Inequalities via theory of time scale; Department of Mathematics, University of Sargodha, October 2014.
  3. SOBIA NAWAZ, Qualitative Properties of Rational Difference Equations; Department of Mathematics, University of Sargodha, October 2014.
  4. RUQAYYA HAFEEZ, Global Behaviour of Non Linear Difference Equations; Department of Mathematics, University of Sargodha, October 2014.
  5. TANVEER AHMED, Hölder and Minkowski inequalities for function of several variables; Department of Mathematics, University of Sargodha, August 2015.
  6. UZMA SADAF, Refinement of Jensen’s Operator’s inequality; Department of Mathematics, University of Sargodha, September 2015.
  7. NASIRA KAUSAR, Dynamic inequalities of Hardy type via time scales; Department of Mathematics, University of Sargodha, February 2016.
  8. SUMAIYA MALIK, Analytic behaviour of plant-herbivore and discrete predator-prey models; Department of Mathematics, University of Sargodha, September 2016.
  9. MADIHA, Infectious disease model by incidence rates; Department of Mathematics, University of Sargodha, February 2017.
  10. IKRAM ULLAH, Classical inequalities for diamond alpha integrals on time scales; Department of Mathematics, University of Sargodha (Mandi Bahau Din Campus), May 2017.
  11. ISHRAT FATIMA, Jessen's Inequality for Isotonic Linear Functionals via Time Scales, Department of Mathematics, University of Sargodha, October 2017.
  12. M. RASHID MAJID, Integral Analogue of Popoviciu's Inequality, Department of Mathematics, University of Sargodha (Lyallpur Campus Faisalabad), October 2017.
  13. 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.
  14. MEHAK MUSHTAQ, Some Applications of Hamy Symmetric Functions, Department of Mathematics, University of Sargodha, March 2018.
  15. ALIA RAMZAN, Dynamic Opial inequalities on time scales, Department of Mathematics, University of Sargodha, January 15, 2019.
  16. BISMA KAZMI, Ostrowski and Hausdroff Type Inequalities via Time Scale Calculus, Department of Mathematics, University of Sargodha, February 18, 2019.
  17. SADAF BASHIR, Mixed Symmetric Means related to new Refinements of Discrete Holder's Inequality, Department of Mathematics, University of Sargodha, February 18, 2019.
  18. TAHREEM ABBAS, Hardy-Hilbert Type Inequalities via Diamond Integrals, Department of Mathematics, University of Sargodha, December 17, 2019.
  19. ALI ASGHAR, Some Hardy-Type Inequalities via Diamond-Alpha Integrals, Department of Mathematics, University of Sargodha, December 17, 2019.
  20. NADIA SAIF, Sharp Inequalities involving Euler’s Gamma Function; Department of Mathematics, University of Sargodha (Ex-PPP Women Campus Faisalabad), December 17, 2019.
  21. AYESHA TARIQ, Hilbert type Inequalities for Multiple Integrals; Department of Mathematics, University of Sargodha (Ex-PPP Women Campus Faisalabad), December 17, 2019.
  22. SONIA MARIUM, Some Extensions of Cauchy Schwarz Inequality; Department of Mathematics, University of Sargodha (Ex-PPP Women Campus Faisalabad), December 17, 2019.
  23. 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.
  24. Awais Rasheed, Inequalities on time scales via interpolating polynomials; Department of Mathematics, University of Sargodha, September 02, 2020.
  25. Muhammad Bilal, Hardy type inequalities for multiple integrals via theory of time scales, Department of Mathematics, University of Sargodha, September 02, 2020.

SIGNIFICANCE

  • COORDINATOR, POST-GRADUATE PROGRAM, DEPARTMENT OF MATHEMATICS, 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

  • Calculus


Courses Taught (Undergraduate Level)

  • Set Theory & ODEs
  • Calculus
  • Partial Differential Equations
  • Topology
  • Measure Theory
  • Functional Analysis

Courses Taught (Postgraduate Level)

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

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