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Journals / Advances in the Theory of Nonlinear Analysis and its Application / 2022 / Cilt: 6 Sayı: 4

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

Sehie Park(The National Academy of Sciences, Republic of Korea, Seoul 06579; and Department of Mathematical Sciences, Seoul National University, Seoul 08826)
Pages
420–432
Publication Date
2022-12-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Such theorems are the ones due to Banach, Nadler, Browder-Göhde-Kirk, Caristi-Kirk, Caristi, Brøndsted, and possibly many others.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Recently, we improved our long-standing Metatheorem in Fixed Point Theory.
📊
Key Findings & Data: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.
💡
Conclusion & Impact:Such theorems are the ones due to Banach, Nadler, Browder-Göhde-Kirk, Caristi-Kirk, Caristi, Brøndsted, and possibly many others.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:fixed point theorem · pre-order metric space · fixed point

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.

🔖

Cite This Article

Park, S. (2022). Equivalents of Ordered Fixed Point Theorems of Kirk, Caristi, Nadler, Banach, and others. Advances in the Theory of Nonlinear Analysis and its Application, Cilt: 6 Sayı: 4, 420–432. https://doi.org/10.31197/atnaa.1127248

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