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Fixed point theorem for nonexpansive semigroups on Banach space. (English) Zbl 0818.47055

Summary: Let \(C\) be a nonempty closed convex subset of a uniformly convex Banach space, and let \(S\) be a semitopological semigroup such that \(\text{RUC}(S)\) has a left invariant submean. Then we prove a fixed point theorem for a continuous representation of \(S\) as nonexpansive mappings on \(C\).

MSC:

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H20 Semigroups of nonlinear operators
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