Istances and Br\o ndsted's variational principle

TL;DR

This paper extends fundamental variational principles and fixed point theorems using the concept of istance in uniform spaces, providing more general and precise formulations.

Contribution

It introduces novel extensions of Brøndsted's and Ekeland's variational principles and fixed point theorems based on the notion of istance in uniform spaces.

Findings

Extended variational principles with broader applicability

Generalized fixed point theorems with improved precision

Framework based on the concept of istance in uniform spaces

Abstract

The manuscript contains elegant extensions of the fundamental variational principles: Br\o ndsted's and Ekeland's. On the other hand we get general and precise version of the Takahashi and the Cariste fixed point theorems. The results are based on the notion of istance for uniform spaces.