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

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

Blog Article

We prove a version of the Ekeland Variational Principle (EkVP) in a weighted graph G and RHODIOLA 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 Sports 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.