Variational principles in quasi-uniform spaces and quasi-gauge spaces

Abstract

In this article, we obtain an extension of the Ekeland variational principle in quasi-uniform spaces. Since the Ekeland variational principle is a type of perturbed optimization problem, the perturbations do not need to satisfy the triangle property to obtain results. We also give some equivalent results of our main results. Moreover, we present a new version of the Ekeland variational principle and its equivalent results, in the setting of quasi-gage spaces. Finally, we establish the Ekeland variational principle in a (metric) modular space as an application of our results. © 2025 Informa UK Limited, trading as Taylor & Francis Group.