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A Fixed Point Theorem and the Existence of a Haar Measure for Hypergroups Satisfying Conditions Related to Amenability

Published online by Cambridge University Press:  20 November 2018

Benjamin Willson
Benjamin Willson*
Affiliation:
Department of Mathematics, Hanyang University, zzz Wangsimni-ro, Seongdong-gu, Seoul, Korea. e-mail: bwillson@ualberta.ca
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Abstract

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In this paperwe present a fixed point property for amenable hypergroups that is analogous to Rickert’s fixed point theorem for semigroups. It equates the existence of a left invariant mean on the space of weakly right uniformly continuous functions to the existence of a fixed point for any action of the hypergroup. Using this fixed point property, certain hypergroups are shown to have a left Haar measure.

Keywords

43A6243A0543A07invariant measureHaar measurehypergroupamenabilityfunction translations
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 2 , 01 June 2015 , pp. 415 - 422
Copyright
Copyright © Canadian Mathematical Society 2015

References

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