Asymptotically non-expansive actions of strongly amenable semigroups and fixed points

Aminpour, A. M.; Dianatifar, A.; Nasr-Isfahani, Rasoul

doi:10.1016/j.jmaa.2017.12.061

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“…Note that if a semitopological semigroup S is left reversible, then AP(S) has a left invariant mean and the converse is false. For other related results, we refer the readers to [1,5,13,18,20,21,31].…”

Section: Introductionmentioning

confidence: 99%

Existence of fixed points and retractions for asymptotically nonexpansive semigroups in locally convex spaces

Bakhande

Saeidi

2019

J. Fixed Point Theory Appl.

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In this paper, we will be concerned with a problem raised by Lau (Fixed Point Theory Appl, 2010) for the existence of common fixed points for a right reversible semitopological semigroup S acting asymptotically nonexpansive on a nonempty compact convex set in the framework of locally convex spaces. We give answers to this problem under the left amenability of ARUC(S) and LMC(S) and then study the existence of Q-nonexpansive retractions in the pointwise closure of S using a new method.

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