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 Gˆateaux 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.

Keywords

• common fixed point
• gauge function
• modified mann iteration
• nonex-pansive mapping
• reexive banach space