Generalized Ekeland’s variational principle with applications

Involving w w -distances we prove a fixed point theorem of Caristi-type in the realm of (non-necessarily T 1 {T}_{1} ) quasi-metric spaces. With the help of this result, a characterization of quasi-metric completeness is obtained. Our approach allows us to retrieve several key examples occurring in various fields of mathematics and computer science and that are modeled as non- T 1 {T}_{1} quasi-metric spaces. As an application, we deduce a characterization of complete G G -metric spaces in terms of a weak version of Caristi’s theorem that involves a G-metric version of w-distances.

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Characterizations of quasi-metric and G-metric completeness involving w-distances and fixed points

Karapınar

Romaguera

Tirado

2022

Demonstratio Mathematica

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Generalized Ekeland’s variational principle with applications

Abstract: By using the concept of Γ-distance, we prove EVP (Ekeland's variational principle) on quasi-F-metric (q-F-m) spaces. We apply EVP to get the existence of the solution to EP (equilibrium problem) in complete q-F-m spaces with Γ-distances. Also, we generalize Nadler's fixed point theorem.

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Characterizations of quasi-metric and G-metric completeness involving w-distances and fixed points

Characterizations of quasi-metric and G-metric completeness involving w-distances and fixed points

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