Kirk, Caristi, Nadler, Banach等人的有序不动点定理的等价

Advances in the Theory of Nonlinear Analysis and its Application Pub Date : 2022-01-01 DOI:10.31197/atnaa.1127248

Sehie Park

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引用次数: 2

摘要

最近，我们改进了不动点理论中存在已久的元定理。作为应用，本文将一些著名的序理论不动点定理等价地表述为关于极大元、公不动点、公平稳点等的存在性定理。这些定理是由Banach, Nadler, Browder-Göhde-Kirk, Caristi- kirk, Caristi, Brøndsted，可能还有许多其他人提出的。

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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Equivalents of Ordered Fixed Point Theorems of Kirk, Caristi, Nadler, Banach, and others

Recently, we improved our long-standing Metatheorem in Fixed Point Theory. In this paper, as its applications, some well-known order theoretic fixed point theo- rems are equivalently formulated to existence theorems on maximal elements, com- mon fixed points, common stationary points, and others. Such theorems are the ones due to Banach, Nadler, Browder-Göhde-Kirk, Caristi-Kirk, Caristi, Brøndsted, and possibly many others.

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Advances in the Theory of Nonlinear Analysis and its Application

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