A Fixed Point Theorem and the Existence of a Haar Measure for Hypergroups Satisfying Conditions Related to Amenability
Printed: Jun 2015
In this paper we present a fixed point property for amenable
hypergroups which 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, a certain class of hypergroups
are shown to have a left Haar measure.
invariant measure, Haar measure, hypergroup, amenability, function translations
43A62 - Hypergroups
43A05 - Measures on groups and semigroups, etc.
43A07 - Means on groups, semigroups, etc.; amenable groups