Attractive Point and Weak Convergence Theorems for Two Commutative Nonlinear Mappings in Banach Spaces (The deepening of function spaces and its environment)

Abstract

In this article, using the class of generalized nonspreading mappings in Banach spaces which covers generalized hybrid mappings in a Hilbert space, we prove an attractive point theorem. Furthermore, we prove a nonlinear mean convergence theorem of Baillon's type and a weak convergence theorem of Mann's type for generalized nonspreading mappings in a Banach space. Using these theorems, we obtain new attractive point theorems, mean convergence theoretns and weak convergence theorems in Hilbert spaces and Banach spaces.