Strong convergence theorems for a sequence of nonexpansive mappings with gauge functions

Abstract

In this paper, we first prove a path convergence theorem for a nonexpansive mapping in a reflexive and strictly convex Banach space which has a uniformly Gâteaux differentiable norm and admits the duality mapping jφ, where φ is a gauge function on [0, ∞). Using this result, strong convergence theorems for common fixed points of a countable family of nonexpansive mappings are established.