Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 363257, 17 pages
Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces
Department of Mathematics, University of Kurdistan, Sanandaj 416, Kurdistan 66196-64583, Iran
Received 16 August 2008; Accepted 10 December 2008
Academic Editor: Mohamed Khamsi
Copyright © 2008 Shahram Saeidi. 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.
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 into 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 , , and be sequences in (0, 1) such that , for all . 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 .