scholarly journals Invariant means and fixed point properties for non-expansive representations of topological semigroups

1995 ◽  
Vol 5 (1) ◽  
pp. 39 ◽  
Author(s):  
Wataru Takahashi ◽  
Anthony To-Ming Lau
Keyword(s):  
Fixed Point ◽  
Topological Semigroups ◽  
Fixed Point Properties ◽  
Invariant Means

Invariant means and fixed point properties on completely regular spaces

1977 ◽  
Vol 16 (2) ◽  
pp. 203-212
Author(s):  
Marvin W. Grossman
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Topological Semigroup ◽  
Related Result ◽  
Continuous Functions ◽  
Point Property ◽  
Completely Regular ◽  
Fixed Point Properties ◽  
Bounded Functions ◽  
Invariant Means

Two theorems are presented which characterize the existence of multiplicative left invariant means on a given algebra of unbounded continuous functions on a topological semigroup S in terms of certain common fixed point properties of actions of S on completely regular spaces. Also a lattice formulation of a related result of Theodore Mitchell for the case of bounded functions is shown to be equivalent to a certain common fixed point property on Bauer simplexes.

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

2020 ◽  
pp. 1-12
Author(s):  
KHADIME SALAME
Keyword(s):  
Fixed Point ◽  
Topological Spaces ◽  
Compact Groups ◽  
Locally Convex Spaces ◽  
Locally Compact ◽  
Completely Regular ◽  
Continuous Mappings ◽  
Fixed Point Properties ◽  
Invariant Means ◽  
Locally Convex

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.

Strong and pure fixed point properties of mappings on normed spaces

2021 ◽  
Author(s):  
Hüseyin Işık ◽  
Vahid Parvaneh ◽  
Mohammad Reza Haddadi
Keyword(s):  
Fixed Point ◽  
Normed Spaces ◽  
Fixed Point Properties
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