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On Ekeland’s variational principle in \(b\)-metric spaces. (English) Zbl 1278.54022
The concept of \(b\)-metric spaces was formulated by I. A. Bakhtin in [Funkts. Anal. 30, 26–37 (1989; Zbl 0748.47048)], which is an extension of the concept of the ordinary metric spaces. In this paper, the authors build a new version of Ekeland’s variational principle in \(b\)-metric spaces. Using this result, they obtain a Caristi type fixed point theorem for self-mappings in complete \(b\)-metric spaces.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54E50 Complete metric spaces
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