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Journals / Advances in the Theory of Nonlinear Analysis and its Application / 2026 / Cilt: 7 Sayı: 1

Applications of Several Minimum Principles

Sehie Park(The National Academy of Sciences, Republic of Korea; Seoul 06579)
Pages
52–60
Publication Date
2023-03-31
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AI Summary & Key Takeaways

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

We show that known examples due to Zorn (1935), Kasahara (1976), Brézis-Browder (1976), Taskovi¢ (1989), Zhong (1997), Khamsi (2009), Cobzas (2011) and others can be improved and strengthened by our new minimum principles.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In our previous works, a Metatheorem in ordered fixed point theory showed that certain maximum principles can be reformulated to various types of fixed point theorems for progressive maps and conversely.
📊
Key Findings & Data:Therefore, there should be the dual principles related to minimality, anti-progressive maps, and others.
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Conclusion & Impact:We show that known examples due to Zorn (1935), Kasahara (1976), Brézis-Browder (1976), Taskovi¢ (1989), Zhong (1997), Khamsi (2009), Cobzas (2011) and others can be improved and strengthened by our new minimum principles.
🔬Design:Araştırma Makalesi
📍Scope:2009 Verileri
⚙️Variables:The 2023 Metatheorem · Brøndsted-Jachymski Principle · Zorn's Lemma

Abstract

In our previous works, a Metatheorem in ordered fixed point theory showed that certain maximum principles can be reformulated to various types of fixed point theorems for progressive maps and conversely. Therefore, there should be the dual principles related to minimality, anti-progressive maps, and others. In the present article, we derive several minimum principles particular to Metatheorem and their applications. One of such applications is the Brøndsted-Jachymski Principle. We show that known examples due to Zorn (1935), Kasahara (1976), Brézis-Browder (1976), Taskovi¢ (1989), Zhong (1997), Khamsi (2009), Cobzas (2011) and others can be improved and strengthened by our new minimum principles.

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Cite This Article

Park, S. (2023). Applications of Several Minimum Principles. Advances in the Theory of Nonlinear Analysis and its Application, Cilt: 7 Sayı: 1, 52–60. https://doi.org/10.31197/atnaa.1204381

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References (24)

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