Weak and strong convergence to common fixed points of a countable family of multi-valued mappings in Banach spaces

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. © 2011 by the Mathematical Association of Thailand.