A Survey on Approximation of Common Fixed Point of Countably Infinite Family of Nonexpansive Mappings

Abstract

In this paper, strong convergence theorems for approximation of a common fixed point of countably family of nonexpansive mappings in strictly convex reflexive real Banach space with uniformly Gâteaux differentiable norm are proved. Consequently, strong convergence theorems for approximation of a common fixed point of countably infnite family of k-strictly pseudocontractive mappings are proved in strictly convex q-uniformly smooth real Banach spaces. Numerical example is generated to demonstrate workability of an algorithm developed. Our theorems extend, improve and generalize some existing results.