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Completeness in quasi-metric spaces and Ekeland variational principle. (English) Zbl 1217.54026
The author establishes a quasi-metric version of the Ekeland variational principle and studies its connections with the completeness properties of the underlying quasi-metric space. The equivalence with Caristi-Kirk’s fixed point theorem and a proof of Clarke’s fixed point theorem for directional contractions within this framework are also investigated. In the reference section, the author enlists many germane articles on the subject discussed.

MSC:
54E15 Uniform structures and generalizations
54E50 Complete metric spaces
54E55 Bitopologies
49N99 Miscellaneous topics in calculus of variations and optimal control
58E30 Variational principles in infinite-dimensional spaces
47H10 Fixed-point theorems
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