Nonexpansive, -continuous antirepresentations have common fixed points

Author:
Wojciech Bartoszek

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1051-1055

MSC (1991):
Primary 47H10, 22A25; Secondary 28D05

DOI:
https://doi.org/10.1090/S0002-9939-99-04567-0

MathSciNet review:
1469398

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Abstract: Let be a closed convex subset of a Banach (dual Banach) space . By we denote an antirepresentation of a semitopological semigroup as nonexpansive mappings on . Suppose that the mapping is jointly continuous when has the weak (weak*) topology and the Banach space of bounded right uniformly continuous functions on has a right invariant mean. If is weakly compact (for some the set is weakly* compact) and norm separable, then has a common fixed point in .

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Additional Information

**Wojciech Bartoszek**

Affiliation:
Department of Mathematics, University of South Africa, P.O. Box 392, Pretoria 0003, South Africa

Email:
bartowk@alpha.unisa.ac.za

DOI:
https://doi.org/10.1090/S0002-9939-99-04567-0

Keywords:
Fixed point,
topological semigroup,
nonexpansive mapping

Received by editor(s):
July 14, 1997

Communicated by:
Dale Alspach

Article copyright:
© Copyright 1999
American Mathematical Society