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We 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… Click to show full abstract
We 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.
Keywords:
completeness;
ekeland variational;
osc property;
principle;
weighted graph;
variational principle
Journal Title: Axioms
Year Published: 2023
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Journal Title: Axioms
Year Published: 2023
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!