Applications of Several Minimum Principles

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.