Abstract
Let $S$ be a right reversible semitopological semigroup, and let ${\rm LUC}(S)$ be the space of left uniformly continuous functions on $S$. Suppose that ${\rm LUC}(S)$ 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.
Citation
Bui Ngoc Muoi. Ngai-Ching Wong. "Fixed point theorems of various nonexpansive actions of semitopological semigroups on weakly/weak* compact convex sets." Topol. Methods Nonlinear Anal. 59 (2B) 1047 - 1067, 2022. https://doi.org/10.12775/TMNA.2021.050
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