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Dergiler / 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)
Sayfa
52–60
Yayın Tarihi
2023-03-31
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri:Therefore, there should be the dual principles related to minimality, anti-progressive maps, and others.
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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:2009 Verileri
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (24)

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  23. M.R. Taskovi¢, On an equivalent of the axiom of choice and its applications, Math. Jpn. 31(6) (1986), 979-991.
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