Equivalents of Certain Minimal Element Principles
Keywords:
Nonlinear neutral differential equations, periodic solutions, fixed point theorem, distributed delaysAbstract
In this article, by applying our 2023 Metatheorem in ordered fixed point theory, we obtain various Minimal Element Principles with their equivalent formulations to existence theorems on minimal elements, common fixed points, common stationary points, and others. Some known theorems and new ones appear in such equivalents. 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 substantially strengthened.References
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