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<p>This paper is concerned with the extension to semigroups two interesting results by Vijayaraju that guarantee the existence of a fixed point for asumptotically nonexpansive and uniformly asymptotically regular mappings on a star-shaped set in a separated locally convex space. We prove that those results are extensible to the class of (left) reversible topological semigroups <i>S</i> and can be improved significantly by dropping some conditions, and study some related results in connection with amenability of AP(<i>S</i>) and WAP(<i>S</i>).</p>

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Reversible topological semigroups of uniformly asymptotically regular mappings on locally convex spaces

  • 期刊论文

  • 发表日期：

    2025年11月7日

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  • Khadime Salame

摘要

This paper is concerned with the extension to semigroups two interesting results by Vijayaraju that guarantee the existence of a fixed point for asumptotically nonexpansive and uniformly asymptotically regular mappings on a star-shaped set in a separated locally convex space. We prove that those results are extensible to the class of (left) reversible topological semigroups S and can be improved significantly by dropping some conditions, and study some related results in connection with amenability of AP(S) and WAP(S).