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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Subrahmanyam, P.V. (2018). Caristi’s Fixed Point Theorem. In: Elementary Fixed Point Theorems. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-13-3158-9_7
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DOI: https://doi.org/10.1007/978-981-13-3158-9_7
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