Open Access

Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces

Fixed Point Theory and Applications20092008:363257

https://doi.org/10.1155/2008/363257

Received: 16 August 2008

Accepted: 10 December 2008

Published: 1 February 2009

Abstract

Let be a left amenable semigroup, let be a representation of as Lipschitzian mappings from a nonempty compact convex subset of a smooth Banach space E into C with a uniform Lipschitzian condition, let be a strongly left regular sequence of means defined on an -stable subspace of , let be a contraction on , and let be sequences in (0, 1) such that , for all n. Let , for all . Then, under suitable hypotheses on the constants, we show that converges strongly to some in , the set of common fixed points of , which is the unique solution of the variational inequality , for all .

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Authors’ Affiliations

(1)
Department of Mathematics, University of Kurdistan

Copyright

© Shahram Saeidi. 2008

This article is published under license to BioMed Central Ltd. 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.