Approximating common fixed points of families of quasi-nonexpansive mappings

Abstract

This paper deals with a family of quasi-nonexpansive mappings in a uniformly convex Banach space, and the convergence of iterates generated by this family. A fixed point theorem for two quasi-nonexpansive mappings is then proved. This theorem is then extended for a finite family of quasinonexpansive mappings. It is shown that Ishikawa's [1] result follows as special cases of results proved in this paper.

Keywords

• uniformly convex Banach spaces
• fixed point theorems
• families of quasi-nonexpansive mappings
• and convergence of iterates.