## 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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