Applications of Several Minimum Principles

Authors : Sehie PARK

Pages : 52-60

Doi:10.31197/atnaa.1204381

View : 124 | Download : 138

Publication Date : 2023-03-31

Article Type : Research Paper

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 insert ignore into journalissuearticles values(1935);, Kasahara insert ignore into journalissuearticles values(1976);, Brézis-Browder insert ignore into journalissuearticles values(1976);, Taskovi¢ insert ignore into journalissuearticles values(1989);, Zhong insert ignore into journalissuearticles values(1997);, Khamsi insert ignore into journalissuearticles values(2009);, Cobzas insert ignore into journalissuearticles values(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