Strong Convergence Theorems for a Common Fixed Point of Two Countable Families of Relatively Quasi Nonexpansive Mappings and Applications

Abstract

The purpose of this paper is to prove strong convergence theorems for common fixed points of two countable families of relatively quasi nonexpansive mappings in a uniformly convex and uniformly smooth real Banach space using the properties of generalized $f$-projection operator. In order to get the strong convergence theorems, a new iterative scheme by monotone hybrid method is presented and is used to approximate the common fixed points. Then, two examples of countable families of uniformly closed nonlinear mappings are given. The results of this paper modify and improve the results of Li et al. (2010), the results of Takahashi and Zembayashi (2008), and many others.