ARTICLE | doi:10.20944/preprints202301.0484.v1
Subject: Computer Science And Mathematics, Computer Vision And Graphics Keywords: Ekeland variational principle; Takahashi minimization principle; Caristi fixed point theorem; weighted graph; partially ordered metric space; completeness; the OSC property
Online: 26 January 2023 (17:12:51 CET)
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.