Equivalents of Certain Minimal Element Principles

In this article, by applying our 2023 Metatheorem in ordered fixed point theory, we obtain various MinimalElement Principles with their equivalent formulations to existence theorems on minimal elements, commonfixed points, common stationary points, and others. Some known theorems and new ones appear in suchequivalents. Consequently, dual versions of the Ekeland principle (1972-74), the Caristi theorem (1976,1979), works of Bae-Park (1983), Takahashi (1991), Lin-Du (2008), Cobzaş (2022), and others are substan-tially strengthened.