Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces
Shahram Saeidi · Fixed Point Theory and Applications · 2009
Abstract Let "Equation missing" be a left amenable semigroup, let "Equation missing" be a representation of "Equation missing" as Lipschitzian mappings from a nonempty compact convex subset "Equation missing" of a smooth Banach space E into C with a uniform Lipschitzian condition, let "Equation missing" be a strongly left regular sequence of means defined on an "Equation missing"-stable subspace of "Equation missing", let "Equation missing" be a contraction on "Equation missing", and let "Equation missing" be sequences in (0, 1) such that "Equation missing", for all n. Let "Equation missing", for all "Equation missing". Then, under suitable hypotheses on the constants, we show that "Equation missing" converges strongly to some "Equation missing" in "Equation missing", the set of common fixed points of "Equation missing", which is the unique solution of the variational inequality "Equation missing", for all "Equation missing".