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

Year 2022, Volume: 6 Issue: 4, 420 - 432, 30.12.2022

Sehie Park

https://doi.org/10.31197/atnaa.1127248

Cited By: 2

Abstract

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.

Keywords

fixed point theorem, pre-order metric space, fixed point, stationary point, stationary point, maximal element

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