Equivalents of maximum principles for several spaces

Author:

Park Sehie1

Affiliation:

1. The National Academy of Sciences, Republic of Korea ; Seoul and Department of Mathematical Sciences , Seoul National University , Seoul , Korea , sehiepark@gmail.com; parksehie.com

Abstract

Abstract According to our long-standing Metatheorem, certain maximum theorems can be equivalently reformulated to various types of fixed point theorems, and conversely. As examples of such theorems, in this paper, we list Zermelo’s fixed point theorem, Brøndsted’s principle, Fang’s F-type theorem, related theorems for locally convex spaces and quasi-uniform spaces. Further we review some few works concerned with our Metatheorem.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Geometry and Topology,Algebra and Number Theory

Reference21 articles.

1. [1] S. Park, Equivalents of various maximum principles, Results in Nonlinear Analysis 5 (2022), 169–174.

2. [2] S. Park, Some applications of Ekeland’s variational principle to fixed point theory, Approximation Theory and Applications (S.P. Singh, ed.), Pitman Res. Notes Math. 133 (1985), 159–172.

3. [3] S. Park, Countable compactness, l.s.c. functions, and fixed points, J. Korean Math. Soc. 23 (1986), 61–66.

4. [4] S. Park, Equivalent formulations of Ekeland’s variational principle for approximate solutions of minimization problems and their applications, Operator Equations and Fixed Point Theorems (S.P. Singh et al., eds.), MSRI-Korea Publ. 1 (1986), 55–68.

5. [5] S. Park, Equivalent formulations of Zorn’s lemma and other maximmumm principles, J. Korean Soc. Math. Edu. 25 (1987), 19–24.

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