Super Asymptotically Nonexpansive Actions of Semitopological Semigroups on Frechet and Locally Convex Spaces

Bui Ngoc Muoi, Ngai-Ching Wong

备注：: arXiv admin note: text overlap with arXiv:2006.15393
发表信息：: Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis (Hakodate, Japan, 2019)

英文摘要：

Let LUC$(S)$ be the space of left uniformly continuous functions on a semitopological semigroup $S$. Suppose that $S$ is right reversible and $\operatorname{LUC}(S)$ has a left invariant mean. Let $(X,d)$ be a Fréchet space. Let $τ$ be a locally convex topology of $X$ weaker than the $d$-topology such that the metric $d$ is $τ$-lower semicontinuous. Let $K$ be a $d$--separable and $τ$--compact convex subset of $X$. We show that every jointly $τ$-continuous and super asymptotically $d$-nonexpansive action $S\times K\mapsto K$ of $S$ has a common fixed point. Similar results in the locally convex space setting are provided.

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