MTH604: Fixed Point Theory and Applications

This course is intended as a brief introduction to the subject with a focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equations, nonlinear integral equations, real and complex implicit functions theorems and system of nonlinear equations. Some generalizations and similar results e. g. Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued mappings are also educated.

Basic concepts: metric spaces, complete metric spaces, Vector spaces (linear spaces) normed spaces, Banach spaces, Banachs contraction principle, non-expansive mappings and related fixed point theorems. Contractive maps, properties of fixed points set and minimal sets. Multi-valued mappings and related fixed point theorems. Best approximation theorems.

  1. B. Bollobas: W. Fulton, A. Katok, F. Kirwan and P. Sarnak: Fixed Point Theory and Applications, Cambridge University Press, 2001.
  2. K. Geoble and W.A Kirk: Topics in Metric Fixed Theory, Cambridge university Press, 1990
  3. M.C. Joshi And R.K. Bose: Some Topics in Nonlinear Functional Analysis, John Wiley and Sons, 1985
  4. James Dugundji and A. Granas: Fixed Point Theory, Vol. 1, Polish Scientific Publishers, 1982
  5. W.A. Kirk and B. Sims: Handbook of Metric Fixed Point Theory, Klawer Academic Publishers 2001
  6. M. Aslam Noor, Principles of Variational Inequalities Lapt-Lambert Academic Publishing AG & Co. Saarbrucken, Germany 2009.