Applications of Several Minimum Principles

Year 2023, Volume: 7 Issue: 1, 52 - 60, 31.03.2023

Sehie Park

https://doi.org/10.31197/atnaa.1204381

Cited By: 1

Abstract

In our previous works, a Metatheorem in ordered fixed point theory showed that certain maximum principles
can be reformulated to various types of fixed point theorems for progressive maps and conversely. Therefore,
there should be the dual principles related to minimality, anti-progressive maps, and others. In the present
article, we derive several minimum principles particular to Metatheorem and their applications. One of
such applications is the Brøndsted-Jachymski Principle. We show that known examples due to Zorn (1935),
Kasahara (1976), Brézis-Browder (1976), Taskovi¢ (1989), Zhong (1997), Khamsi (2009), Cobzas (2011) and
others can be improved and strengthened by our new minimum principles.

Keywords

The 2023 Metatheorem, Brøndsted-Jachymski Principle, Zorn's Lemma, Caristi fixed point theorem, Ekeland variational principle, preorder, fixed point, stationary point, minimum principle

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