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Let X be a uniformly convex Banach space and \(C \subset X\) be bounded, closed, and convex. In this chapter, we prove that, in this context, every asymptotic pointwise contractive semigroup possesses a unique common fixed point in C, which can be constructed by taking the strong limit of orbits. Furthermore, we demonstrate that every asymptotic pointwise nonexpansive semigroup has at least one fixed point in C and that the set of all common fixed points is closed and convex.

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Existence of Common Fixed Points for Pointwise Lipschitzian Semigroups

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  • 发表日期：

    2026年

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  • Wojciech M. Kozlowski

摘要

Let X be a uniformly convex Banach space and \(C \subset X\) be bounded, closed, and convex. In this chapter, we prove that, in this context, every asymptotic pointwise contractive semigroup possesses a unique common fixed point in C, which can be constructed by taking the strong limit of orbits. Furthermore, we demonstrate that every asymptotic pointwise nonexpansive semigroup has at least one fixed point in C and that the set of all common fixed points is closed and convex.