Common Fixed Points of an Iterative Method for Berinde Nonexpansive Mappings

Abstract

A mapping T form a nonempty closed convex subset $C$ of a uniformly Banach space into itself is called a Berinde nonexpansive mapping if there is $L\geq 0$ such that $\norm{Tx-Ty}\leq \norm{x-y}+L\norm{y-Tx}$ for any $x, y\in C$. In this paper, we prove weak and strong convergence theorems of an iterative method for approximating common fixed points of two Berinde nonexpansive mappings under some suitable control conditions in a Banach space. Moreover, we apply our results to equilibrium problems and fixed point problems in a Hilbert space.