Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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EXTENSIONS OF ORDERED FIXED POINT THEOREMS

  • Sehie Park (The National Academy of Sciences, Department of Mathematical Sciences, Seoul National University)
  • Received : 2022.12.30
  • Accepted : 2023.06.25
  • Published : 2023.09.15
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Abstract

Our long-standing Metatheorem in Ordered Fixed Point Theory is applied to some well-known order theoretic fixed point theorems. In the first half of this article, we introduce extended versions of the Zermelo fixed point theorem, Zorn's lemma, and the Caristi fixed point theorem based on the Brøndsted-Jachymski principle and our 2023 Metatheorem. We show some of their applications to other fixed point theorems or theorems on the existence of maximal elements in partially ordered sets. In the second half, we collect and improve order theoretic fixed point theorems in the collection of Howard-Rubin in 1991 and others. In fact, we improve or extend several ordering principles or fixed point theorems due to Brézis-Browder, Brøndsted, Knaster-Tarski, Tarski-Kantorovitch, Turinici, Granas-Horvath, Jachymski, and others.

Keywords

References

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