Weak and Strong Convergence Theorems for Two Commutative Nonlinear Mappings in Banach Spaces (Nonlinear Analysis and Convex Analysis)

Abstract

In this article, we first prove a mean convergence theorem of Baillon's type iteration for finding a common fixed point of commutative 2-generahzed nonspreading mappings in a Banach space. Furthermore, we obtain a weak convergence theorem of Mann's type iteration for finding a common fixed point of the mappings in a Banach space. We also prove a strong convergence theorem of Halpern's type iteration for finding a common fixed point of the mappings in a Banach space. Using these results, we get well-known and new weak and strong convergence theorems in a Hilbert space and a Banach space.