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Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces
Fixed Point Theory and Applications volume 2008, Article number: 363257 (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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Saeidi, S. Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces. Fixed Point Theory Appl 2008, 363257 (2009). https://doi.org/10.1155/2008/363257
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DOI: https://doi.org/10.1155/2008/363257