戈贝尔-柯克定理的模块化版本

Pub Date : 2024-03-10 DOI:10.12775/tmna.2023.059

Wojciech M. Kozlowski

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引用次数: 0

摘要

在本文中，我们证明了作用于模态空间的渐近非展开映射的定点定理。这一结果概括了 K. Goebel 和 W.A. Kirk 于 1972 年提出的定点定理。在此过程中，我们将其他几个结果（包括 Milman-Pettis 定理）从巴纳赫空间类扩展到更大的正则模态空间类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Modular version of Goebel-Kirk theorem

In this paper we prove a fixed point theorem for asymptotically nonexpansive mappings acting in modular spaces. This result generalises the 1972 fixed point theorem by K. Goebel and W.A. Kirk. In the process, we extend several other results (including the Milman-Pettis theorem) from the class of Banach spaces to the larger class of regular modular spaces.

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