Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces
© Shahram Saeidi. 2008
Received: 16 August 2008
Accepted: 10 December 2008
Published: 1 February 2009
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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