Equivalents of maximum principles for several spaces

Abstract

According to our long-standing Metatheorem, certain maximum theorems can be equivalently reformulated to various types of fixed point theorems, and conversely. As examples of such theorems, in this paper, we list Zermelo’s fixed point theorem, Brøndsted’s principle, Fang’s F-type theorem, related theorems for locally convex spaces and quasi-uniform spaces. Further we review some few works concerned with our Metatheorem.

Keywords

• ekeland variational principle
• pre-order
• zermelo
• quasi-metric space
• fixed point
• maximal element
• locally convex space
• quasi-uniform space
• 06a75
• 47h10
• 54e35
• 54e50
• 54h25
• 58e30
• 65k10