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

Ali Basit, Stefan Cobzas, Mokhwetha Daniel Mabula
2023 unpublished
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.
doi:10.20944/preprints202301.0484.v1 fatcat:ivycxtsof5cgjn5nfljfatwohi