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arXiv · 2006.15393

Fixed point theorems of various nonexpansive actions of semitopological semigroups on weakly/weak* compact convex sets

Bui Ngoc Muoi·Ngai-Ching Wong
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Abstract

Let $S$ be a right reversible semitopological semigroup, and let $\operatorname{LUC}(S)$ be the space of left uniformly continuous functions on $S$. Suppose that $\operatorname{LUC}(S)$ has a left invariant mean. Let $K$ be a weakly compact convex subset of a Banach space. We show that there always exists a common fixed point for any jointly weakly continuous and super asymptotically nonexpansive action of $S$ on $K$. Several variances involving the weak* compactness, the RNP, the distality of $K$ and/or the left reversibility of $S$ are also provided.

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Bui Ngoc Muoi, Ngai-Ching Wong. 2020-06-27. Fixed point theorems of various nonexpansive actions of semitopological semigroups on weakly/weak* compact convex sets. https://arxiv.org/abs/2006.15393

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