On Fixed Point Iteration Procedures

In this book, we define some iterative procedures namely: Mann and Ishikawa iterations, Mann and Ishikawa iterations with errors, Modified Mann iteration, Perturbed Mann iteration and Viscosity Approximation method which are less frequently used to approximate the fixed points. Besides these, we also present the results which are related to the robustness of Mann algorithm. Chapter 1 is mainly devoted to the background material wherein the classical fixed point theorems such as: Banach Contraction Principle and Kirk Fixed Point Theorem are presented which are also followed by their certain noted generalizations. For proving Kirk Fixed Point Theorem, a relevant material on Normal Structure in Banach Spaces is also presented.