Research Article

Ekeland, Takahashi and Caristi principles in preordered quasi-metric spaces

Published in: Quaestiones Mathematicae
Volume 46 , issue 4 , 2023 , pages: 791–812

DOI: 10.2989/16073606.2022.2042417

Author(s): S. Cobzaş Babeş-Bolyai University, Romania

Keywords: 46N10 , 47H10 , 58E30 , 54E25 , 54E35 , reordered quasi-metric space , completeness in quasi-metric spaces , variational principles , Ekeland variational principle , Takahashi minimization principle , fixed point , Caristi fixed point theorem

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Abstract

We prove versions of Ekeland, Takahashi and Caristi principles in pre-ordered quasi-metric spaces, the equivalence between these principles, as well as their equivalence to some completeness results for the underlying quasi-metric space. These extend the results proved in S. Cobzaş, Topology Appl. 265 (2019), 106831, 22, for quasi-metric spaces.

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