THE MODIFIED MANN ITERATION METHODS FOR AN ASYMPTOTICALLY STRICT PSEUDO-CONTRACTIVE FAMILY IN HILBERT SPACES

摘要

In this paper, we first propose a modified Mann's iteration method for an asymptotically strict pseudo-contractive family of self-mappings defined on a closed convex subset in a Hilbert space. Next we study the weak and strong convergence of modified Mann's iteration method for such an asymptotically strict pseudo-contractive family. And some applications for the parallel algorithm and the cyclic algorithm relating to our main results are added, which extend and improve the corresponding ones due to Lopez Acedo and Xu [Nonlinear Analysis TMA, 67 (2007), 2258-2271] for a finite family of strict pseudo-contractions.