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

2019; Birkhäuser; Volume: 21; Issue: 3 Linguagem: Inglês

10.1007/s11784-019-0712-0

1661-7746

Jafar Bakhande, Shahram Saeidi,

Advanced Banach Space Theory

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 $$\text {ARUC}(S)$$ and $$\text {LMC}(S)$$ and then study the existence of Q-nonexpansive retractions in the pointwise closure of S using a new method.