English

Variational principles using a non-symmetric non-triangular distance

Functional Analysis 2025-04-30 v1 Optimization and Control

Abstract

We consider Borwein-Preiss and Ekeland variational principles using distance functions that neither is symmetric nor enjoy the triangular inequality. All the given results rely exclusively on the convergence and continuity behaviors induced synthetically by the distance function itself without any topological implications. At the end of the paper, we also present two applications; the Caristi fixed point theorem and an existence theorem for equilibrium problems.

Keywords

Cite

@article{arxiv.2504.20575,
  title  = {Variational principles using a non-symmetric non-triangular distance},
  author = {Natthaya Boonyam and Parin Chaipunya and Poom Kumam},
  journal= {arXiv preprint arXiv:2504.20575},
  year   = {2025}
}
R2 v1 2026-06-28T23:15:02.200Z