WEAK AND STRONG CONVERGENCE OF MANN'S-TYPE ITERATIONS FOR A COUNTABLE FAMILY OF NONEXPANSIVE MAPPINGS Song, Yisheng; Chen, Rudong;
Let K be a nonempty closed convex subset of a Banach space E. Suppose (n = 1,2,...) is a uniformly asymptotically regular sequence of nonexpansive mappings from K to K such that F. For , define . If satisfies , we proved that weakly converges to some in the framework of reflexive Banach space E which satisfies the Opial's condition or has differentiable norm or its dual has the Kadec-Klee property. We also obtain that strongly converges to some in Banach space E if K is a compact subset of E or there exists one map satisfy some compact conditions such as T is semi compact or satisfy Condition A or and so on.
uniformly asymptotically regular sequence;a countable family of nonexpansive mappings;weak and strong convergence;Mann's type iteration;