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Amenability and Fixed Point Properties of Semitopological Semigroups in Modular Vector Spaces

Part of: Nonlinear operators and their properties Abstract harmonic analysis

Published online by Cambridge University Press:  16 December 2019

Khadime Salame
Khadime Salame*
Affiliation:
Diourbel, Senegal Email: khadime.salame1313@gmail.com
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Abstract

In this paper, we initiate the study of fixed point properties of amenable or reversible semitopological semigroups in modular spaces. Takahashi’s fixed point theorem for amenable semigroups of nonexpansive mappings, and T. Mitchell’s fixed point theorem for reversible semigroups of nonexpansive mappings in Banach spaces are extended to the setting of modular spaces. Among other things, we also generalize another classical result due to Mitchell characterizing the left amenability property of the space of left uniformly continuous functions on semitopological semigroups by introducing the notion of a semi-modular space as a generalization of the concept of a locally convex space.

Keywords

almost periodic functionamenabilitymodular functionmodular spacesemigroup

MSC classification

Primary: 47H10: Fixed-point theorems
Secondary: 43A07: Means on groups, semigroups, etc.; amenable groups 43A60: Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 3 , September 2020 , pp. 692 - 704
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Copyright
Š Canadian Mathematical Society 2019

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