STRONG CONVERGENCE OF CQ ITERATION FOR ASYMPTOTICALLY NONEXPANSIVE SEMIGROUPS

Abstract

Kim and Xu proved the strong convergence theorems of modified Mann iterations for asymptotically nonexpansive mappings and semigroups on bounded closed convex subset C of a Hilbert space H by the CQ iteration method. The purpose of this paper is to modify the CQ iteration scheme of Kim and Xu, and to prove strong convergence theorems for asymptotically nonexpansive semigroups on closed convex subset C of a Hilbert space H without the condition of boundedness of subset C. The convergence rate of iteration process presented in this paper is faster than the iteration process of Kim and Xu. While, in this article, we did not use the demi-closedness principle .