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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 694783, 9 pages
http://dx.doi.org/10.1155/2014/694783
Research Article

Invariant Means and Reversible Semigroup of Relatively Nonexpansive Mappings in Banach Spaces

Graduate School of Education, Mathematics Education, Kyungnam University, Changwon 631-701, Republic of Korea

Received 9 May 2014; Accepted 1 July 2014; Published 20 July 2014

Academic Editor: Jong Kyu Kim

Copyright © 2014 Kyung Soo Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The purpose of this paper is to study modified Halpern type and Ishikawa type iteration for a semigroup of relatively nonexpansive mappings on a nonempty closed convex subset of a Banach space with respect to a sequence of asymptotically left invariant means defined on an appropriate invariant subspace of , where is a semigroup. We prove that, given some mild conditions, we can generate iterative sequences which converge strongly to a common element of the set of fixed points , where .