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INVARIANT MEANS AND ACTIONS OF SEMITOPOLOGICAL SEMIGROUPS ON COMPLETELY REGULAR SPACES AND APPLICATIONS

Part of: Nonlinear operators and their properties Abstract harmonic analysis

Published online by Cambridge University Press:  10 June 2020

KHADIME SALAME Open the ORCID record for KHADIME SALAME [Opens in a new window]
KHADIME SALAME*
Affiliation:
Diourbel, Senegal email [email protected]
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Abstract

In this paper, we extend the study of fixed point properties of semitopological semigroups of continuous mappings in locally convex spaces to the setting of completely regular topological spaces. As applications, we establish a general fixed point theorem, a convergence theorem and an application to amenable locally compact groups.

Keywords

amenabilitysemigroupscompletely regular spacesfixed point propertiesHaar measure

MSC classification

Primary: 43A07: Means on groups, semigroups, etc.; amenable groups
Secondary: 43A05: Measures on groups and semigroups, etc. 47H10: Fixed-point theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 1 , February 2021 , pp. 162 - 173
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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