Applications of Several 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 principleAbstract
In our previous works, a Metatheorem in ordered fixed point theory showed that certain maximum principlescan 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 presentarticle, we derive several minimum principles particular to Metatheorem and their applications. One ofsuch 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) andothers can be improved and strengthened by our new minimum principles.
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