Weak Convergence Theorem for Infinite Families of Nonlinear Mappings in Banach Spaces (Study on Nonlinear Analysis and Convex Analysis)

Abstract

In this article, we prove a weak convergence theorem of Mann's type iteration for infinite families of extended generalized hybrid mappings in a Banach space satisfying Opial's condition. This theorem solves a problem posed by Hojo and Takahashi [8]. Using this result, we get well-known and new weak convergence theorems in a Banach space. In particular, we obtain a weak convergence theorem of Mann's type iteration for finite families of extended generalized hybrid mappings in a Banach space.