Convergence theorems for infinite family of multivalued quasi-nonexpansive mappings in uniformly convex banach spaces

Abstract

We introduce an iterative method for finding a common fixed point of a countable family of multivalued quasi-nonexpansive mapping { Ti} in a uniformly convex Banach space. We prove that under certain control conditions, the iterative sequence generated by our method is an approximating fixed point sequence of each T i. Some strong convergence theorems of the proposed method are also obtained for the following cases: all Tiare continuous and one of Tiis hemicompact, and the domain K is compact. Copyright © 2012 Aunyarat Bunyawat and Suthep Suantai.