WEAK AND STRONG CONVERGENCE OF MANN'S-TYPE ITERATIONS FOR A COUNTABLE FAMILY OF NONEXPANSIVE MAPPINGS

- Journal title : Journal of the Korean Mathematical Society
- Volume 45, Issue 5, 2008, pp.1393-1404
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2008.45.5.1393

Title & Authors

WEAK AND STRONG CONVERGENCE OF MANN'S-TYPE ITERATIONS FOR A COUNTABLE FAMILY OF NONEXPANSIVE MAPPINGS

Song, Yisheng; Chen, Rudong;

Song, Yisheng; Chen, Rudong;

Abstract

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.

Keywords

uniformly asymptotically regular sequence;a countable family of nonexpansive mappings;weak and strong convergence;Mann's type iteration;

Language

English

Cited by

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