In this paper, we extend the study of fixed point properties of semitopological semigroups of continuous mappings in locally convex spaces to the setting of completely regular topological spaces. As applications, we establish a general fixed point theorem, a convergence theorem and an application to amenable locally compact groups.

中文翻译：

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完全正则空间和应用上的半拓扑半群的不变均值和作用

在本文中，我们将局部凸空间中连续映射的半拓扑半群不动点性质的研究扩展到完全正则拓扑空间的设置。作为应用，我们建立了一个一般不动点定理、一个收敛定理和一个适用于局部紧群的应用。