论文标题
固定点定理的弱/弱/弱*紧凑型凸组的各种非专业动作的固定点定理
Fixed point theorems of various nonexpansive actions of semitopological semigroups on weakly/weak* compact convex sets
论文作者
论文摘要
让$ s $为正确的可逆半流行病学半群，让$ \ operatotorname {luc}（s）$成为$ s $上左均匀连续功能的空间。假设$ \ operatorname {luc}（s）$具有左不变的均值。令$ k $为Banach空间的弱紧凑型凸子集。我们表明，对于$ k $上的$ s $的任何共同连续且超级渐近性的行动，总是存在一个共同的固定点。还提供了一些涉及弱*紧凑性的差异，RNP，$ K $的远处和/或$ S $的左可逆性。
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. 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.
