Equivalents of Various Principles of Zermelo, Zorn, Ekeland, Caristi and Others

Abstract

Motivated by the Ekeland variational principle, we obtained a Metatheorem in 1985-87 stating that some wellknown existence of maximal elements can be equivalently formulated to existence theorems on fixed elements, stationary points, common fixed points, common stationary points, and others. In the present article, we introduce our new 2023 Metatheorem and its applications to various theorems due to Zermelo, Zorn, Ekeland, Caristi, and related results. In fact, this is a historical supplement of our previous article entitled “Foundations of Ordered Fixed Point Theory."