A HYBRID METHOD FOR A COUNTABLE FAMILY OF LIPSCHITZ GENERALIZED ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS AND AN EQUILIBRIUM PROBLEM

- Journal title : Communications of the Korean Mathematical Society
- Volume 28, Issue 2, 2013, pp.335-351
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2013.28.2.335

Title & Authors

A HYBRID METHOD FOR A COUNTABLE FAMILY OF LIPSCHITZ GENERALIZED ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS AND AN EQUILIBRIUM PROBLEM

Cholamjiak, Prasit; Cholamjiak, Watcharaporn; Suantai, Suthep;

Cholamjiak, Prasit; Cholamjiak, Watcharaporn; Suantai, Suthep;

Abstract

In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings and the solutions set of equilibrium problems. Some strong convergence theorems of the proposed iterative scheme are established by using the concept of W-mappings of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings.

Keywords

generalized asymptotically quasi-nonexpansive mapping;hybrid method;common fixed point;strong convergence;W-mapping;

Language

English

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