Fixed point theorems of various nonexpansive actions of semitopological semigroups on weakly/weak* compact convex sets
DOI:
https://doi.org/10.12775/TMNA.2021.050Keywords
Semitopological semigroups, amenability, reversibility, invariant means, asymptotically nonexpansive actions, Radon-Nikodym property, distality, fixed pointsAbstract
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 not necessarily with normal structure. 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.References
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