Equivalents of Ordered Fixed Point Theorems of Kirk, Caristi, Nadler, Banach, and others

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Advances in the Theory of Nonlinear Analysis and its Application
Volume:6 Issue:4
Equivalents of Ordered Fixed Point Theorems of Kirk, Caristi, Nadler, Banach, and others

Equivalents of Ordered Fixed Point Theorems of Kirk, Caristi, Nadler, Banach, and others

Pages : 420-432

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Publication Date : 2022-12-30

Article Type : Research Paper

Abstract :Recently, we improved our long-standing Metatheorem in Fixed Point Theory. In this paper, as its applications, some well-known order theoretic fixed point theo- rems are equivalently formulated to existence theorems on maximal elements, com- mon fixed points, common stationary points, and others. Such theorems are the ones due to Banach, Nadler, Browder-Göhde-Kirk, Caristi-Kirk, Caristi, Brøndsted, and possibly many others.
Keywords : fixed point theorem, pre order metric space, fixed point, stationary point, stationary point, maximal element

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