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

Hashemi, Eshagh; Saadati, Reza

doi:10.3390/math6060093

Cited by 3 publications

(1 citation statement)

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“…Ekeland's principle also leads to an elegant proof of the famous Caristi fixed point theorem [14]. For further generalizations and applications of Ekeland's variational principle we refere to [9,25,32,47] and their references. The aim of this section is first to give a variant of Ekeland's variational principle in S JS -metric spaces and, then derive Caristi fixed point theorem as an application (see [7]).…”

Section: Ekeland's Variational Principlementioning

confidence: 99%

S J S -metric spaces: a survey

Beg,

Roy,

Saha

2024

J. Nonlinear Sci. Appl.

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The aim of this survey article, is to present in one place the recently published results on S JS -metric spaces, their generalizations and applications. We start with S JS -metric spaces and study their properties. Then we deal with abstract S JS -topological spaces induced by S JS -metric and present several classical results including Cantor's intersection theorem. Next the notion of sequentially compactness on S JS -metric spaces and properties of sequentially compact S JS -metric spaces are studied. Some fixed point theorems are obtained for integral type contractive mappings. Finally we prove several new results on fixed point for rational type contractive mappings, obtain Ekeland's variational principle on S JS -metric spaces as an application and in the end also present results regarding best S JS -proximity point with application.

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