无偏序的Ran-Reurings不动点定理的一个简单证明
The Ran-Reurings fixed point theorem without partial order: a simple proof
摘要：
本文的目的是将著名的Ran和Reurings不动点定理推广到具有仅传递的二元关系（不一定是偏序）和关系完备度量的空间。这里提出的论点简单明了。Rakotch和Hu-Kirk将Edelstein的Banach压缩原理推广到可链化的完全度量空间上的局部压缩，并将其推广到Ran-Reurings定理。
英文摘要：
The purpose of this note is to generalize the celebrated Ran and Reurings fixed point theorem to the setting of a space with a binary relation that is only transitive (and not necessarily a partial order) and a relation-complete metric. The arguments presented here are simple and straightforward. It is also shown that extensions by Rakotch and Hu-Kirk of Edelstein's generalization of the Banach contraction principle to local contractions on chainable complete metric spaces derive from the theorem of Ran-Reurings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
