On Ekeland’s variational principle in \(b\)-metric spaces. (English) Zbl 1278.54022

Bota, Monica; Molnár, Andrea; Varga, Csaba

Fixed Point Theory 12, No. 1, 21-28 (2011).

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.

Reviewer: Yongxiang Li (Lanzhou)

MSC:

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

Keywords:

variational principle; fixed point theorem; \(b\)-metric spaces