Ali, BasitCobzas, StefanMabula, M.D.2023-11-132023-11-132023-03Ali, B.; 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. https://doi.org/10.3390/axioms12030247.2075-1860 (online)10.3390/axioms12030247http://hdl.handle.net/2263/93236We prove a version of the Ekeland Variational Principle (EkVP) in a weighted graph G and its equivalence to Caristi fixed point theorem and to the 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 weighted graphs for which one of these principles holds, are also considered.en© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).Ekeland variational principleTakahashi minimization principleCaristi fixed point theoremWeighted graphPartially ordered metric spaceCompletenessOSC propertyEkeland variational principle (EkVP)Article