Common fixed points of an infinite family of nonexpansive mappings in uniformly convex metric spaces

Abstract

We generalize the notion of $K$-mapping due to Kangtunyakarn and Suantai (2009) [1] for an infinite family of nonexpansive mappings on a convex metric space and study some of its useful properties. We also establish strong convergence of a Mann type iterative sequence to a common fixed point of an infinite family of nonexpansive mappings on a uniformly convex metric space.