Ekeland’s Variational Principle and Minimization Takahashi’s Theorem in Generalized Metric Spaces

Eshagh Hashemi and Reza Saadati
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Eshagh Hashemi: Department of Mathematics, College of Basic Sciences, Karaj Branch, Islamic Azad University, Alborz 31485-313, Iran
Reza Saadati: Department of Mathematics, Iran University of Science and Technology, Tehran 16846-13114, Iran

Mathematics, 2018, vol. 6, issue 6, 1-14

Abstract: We consider a distance function on generalized metric spaces and we get a generalization of Ekeland Variational Principle (EVP). Next, we prove that EVP is equivalent to Caristi–Kirk fixed point theorem and minimization Takahashi’s theorem.

Keywords: Ekeland variational principle; minimization theorem; fixed point; ?-function; quasi-G-metric (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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