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Research Article Open access CC BY 4.0

Equivalents of Some Ordered Fixed Point Theorems

Sehie Park

Journal of Advances in Mathematics and Computer Science · pp. 52–67 · Published 21 Jan 2023

10.9734/jamcs/2023/v38i11741

Abstract

Some ordered fixed point theorems on metric spaces are equivalent to completeness and existences of maximal (or minimal) elements, common fixed points, common stationary points, etc. Some known or new theorems related to the Caristi fixed point theorem can be equivalently formulated. Consequently, dual versions of the Ekeland principle, the Caristi theorem, theorems of Bae-Park, Takahashi, Chen-Cho-Yang, Jachymski, Cobzas, and others are substantially improved and strengthened.

The 2023 metatheorem Brndsted-Jachymski principle preorder metric space anti-progressive maps fixed point stationary point maximal element

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Cited by 5

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

Sehie Park · Journal of Advances in Mathematics and Computer Science · 2023

Variants of the New Caristi Theorem

Sehie PARK · Advances in the Theory of Nonlinear Analysis and its Application · 2023

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