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Caristi’s Fixed Point Theorem

  • P. V. SubrahmanyamEmail author
Chapter
Part of the Forum for Interdisciplinary Mathematics book series (FFIM)

Abstract

In 1976, Caristi [4] published a novel generalization of the contraction principle. Using transfinite arguments which was also later simplified by Wong [15]. Brondstedt [3] provided an alternative proof by introducing an interesting partial order. On the other hand, Ekeland [6] established a variational principle whence deducing Caristi’s theorem. Brezis and Browder [2] proved an ordering principle also leading to this fixed point theorem. Subsequently Altman [1], Turinici [14, 15] and others have extended this principle. In this chapter, we discuss some of these as well as proofs of Caristi’s theorem by Kirk [8], Penot [10] and Seigel [11]. That both Ekcland’s principle and Caristi’s theorem characterize completeness is also brought out.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia

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