Super Asymptotically Nonexpansive Actions of Semitopological Semigroups
Bui Ngoc Muoi, Ngai‐Ching Wong · arXiv (Cornell University) · 2020
Let $S$ be a right reversible semitopological semigroup, and let LUC$(S)$ be the space of left uniformly continuous functions on $S$. Suppose that LUC$(S)$ has a left invariant mean. We show that there always exists a common fixed point for any jointly weakly continuous and super asymptotically nonexpansive action $S\times K\mapsto K$ of $S$ on a weakly compact convex subset $K$ of a Banach space. Several variances involving weak* compactness of $K$ and other function spaces on $S$ are also provided.