论文标题
半流行学上的超级渐近行为在特雷希特和本地凸空间上
Super Asymptotically Nonexpansive Actions of Semitopological Semigroups on Frechet and Locally Convex Spaces
论文作者
论文摘要
让Luc $ $（S）$为半综合$ s $ s $的左连续功能的空间。假设$ s $是正确的可逆的，$ \ operatorname {luc}（s）$具有左不变的均值。令$（x，d）$为fréchet空间。让$τ$是$ x $的本地凸形拓扑，比$ d $ - 学位弱，以至于公制$ d $是$τ$ - 较低的半连续性。令$ k $为$ d $ - 可分开和$τ$ - 紧凑型凸子集为$ x $。我们表明，每个共同的$τ$ - 连续和超级渐近$ d $ -nonexpansive action $ s \ times k \ apsto k $ of $ s $ of $ s $都有一个共同的固定点。提供了本地凸空间设置中的类似结果。
Let LUC$(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.
