Common Fixed Points of an Iterative Method for Berinde Nonexpansive Mappings

Limpapat Bussaban, Atichart Kettapun

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 ≥ 0
such that kT x − T yk ≤ kx − yk + Lky − T xk for any x, y ∈ 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.