Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Ekeland Variational Principle and Some of Its Equivalents on a Weighted Graph, Completeness and the Osc Property

Version 1 : Received: 25 January 2023 / Approved: 26 January 2023 / Online: 26 January 2023 (17:12:51 CET)

A peer-reviewed article of this Preprint also exists.

Basit, A.; Cobzaş, Ş.; Mabula, M.D. Ekeland Variational Principle and Some of Its Equivalents on a Weighted Graph, Completeness and the OSC Property. Axioms 2023, 12, 247. Basit, A.; Cobzaş, Ş.; Mabula, M.D. Ekeland Variational Principle and Some of Its Equivalents on a Weighted Graph, Completeness and the OSC Property. Axioms 2023, 12, 247.

Abstract

We prove a version of Ekeland Variational Principle (EkVP) in a weighted graph $G$ and its equivalence to Caristi fixed point theorem and to Takahashi minimization principle. The usual completeness and topological notions are replaced with some weaker versions expressed in terms of the graph $G$. The main tool used in the proof is the OSC property for sequences in a graph. Converse results, meaning the completeness of graphs for which one of these principles holds is also considered.

Keywords

Ekeland variational principle; Takahashi minimization principle; Caristi fixed point theorem; weighted graph; partially ordered metric space; completeness; the OSC property

Subject

Computer Science and Mathematics, Computer Vision and Graphics

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