2021/12/22 by Ştefan Cobzaş, Cobzaş, S.
Mathematics · #46N10 47H10 58E30 54E25 54E35 #FOS: Mathematics #Fixed Point Theorems Analysis #General Mathematics (math.GM)
paper · pdf · doi:10.48550/arxiv.2112.12860
openalex publication_date 2021/12/22 · openalex created_date 2021/12/31 · openalex updated_date 2026/07/28
We prove versions of Ekeland, Takahashi and Caristi principles in preordered 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. The key tools are Picard sequences for some special set-valued mappings on a preordered quasi-metric space X, defined in terms of the preorder and of a function φ on X. Key words: preordered quasi-metric space; completeness in quasi-metric spaces; variational principles; Ekeland variational principle; Takahashi minimization principle; fixed point; Caristi fixed point theorem.