Fixed point theorems of various nonexpansive actions of semitopological semigroups on weakly/weak* compact convex sets - Muoi, Bui Ngoc; Wong, Ngai-Ching (Topological Methods in Nonlinear Analysis, 2022)
Let $S$ be a right reversible semitopological semigroup, and let $\operatorname{LUC}(S)$ be the space ofleft 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 anyjointly 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.