Applications of Several Minimum Principles

Sehie PARK

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Applications of Several Minimum Principles

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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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《Advances in the Theory of Nonlinear Analysis and its Applications》 |2023年第1期|52-60|共9页
作者
Sehie PARK;
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作者单位

The National Academy of Sciences;

Seoul 06579South Korea;

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正文语种英语
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The 2023 Metatheorem; Brøndsted-Jachymski Principle; Zorn's Lemma; Caristi fixed point theorem; Ekeland variational principle; preorder; fixed point; stationary point; minimum principle;

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Applications of Several Minimum Principles

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