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 its equivalence to Caristi fixed Safety Waders point theorem and to the Takahashi minimization principle.The usual completeness and topological notions are replaced with some weaker versions expressed in terms of Twin Mattress and Pillow 2/CN 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.