On Ekeland's variational principle

TL;DR

This paper presents an improved version of Ekeland's variational principle applicable to certain functionals in Banach spaces, yielding almost symmetric points and advancing the theoretical understanding of variational principles.

Contribution

It introduces a novel formulation of Ekeland's variational principle for functionals that do not increase upon polarization, enhancing symmetry properties in Banach spaces.

Findings

Established an improved variational principle for specific functionals.

Demonstrated existence of almost symmetric points in Banach spaces.

Extended the applicability of Ekeland's principle to broader classes of functionals.

Abstract

For proper lower semi-continuous functionals bounded below which do not increase upon polarization, an improved version of Ekeland's variational principle can be formulated in Banach spaces, which provides almost symmetric points.