Weak and Strong Convergence to Common Fixed Points of a Countable Family of Multi-valued Mappings in Banach Spaces

Prasit Cholamjiak, Watcharaporn Cholamjiak, Yeol Je Cho, Suthep Suantai

Abstract

In this paper, we introduce a modified Mann iteration for a countable family of multi-valued mappings. We use the best approximation operator to obtain weak and strong convergence theorems in a Banach space. We apply the main results to the problem of finding a common fixed point of a countable family of nonexpansive multi-valued mappings.