On Ekeland Variational Principle and Its Applications Through Fuzzy Quasi Metric Spaces with Non-Archimedean t-norm

The aim of this article is to introduce the Ekeland variational principle (EVP) and some results in fuzzy quasi metric space (FQMS) under the non-Archimedean \(t\)-norms. In this article, the basic topological properties and a partial order relation are defined on FQMS. Utilizing the Brézis-Browder principle on a partially ordered set, we extend the EVP to FQMS as well. Moreover, we derive Takahashi’s minimization theorem, which ensures the existence of a solution to an optimal problem without taking the help of compactness and convexity properties on the underlying space. Furthermore, we give an equivalence chain between these two theorems. Finally, two fixed point results, namely the Banach fixed point and the Caristi-Kirk fixed point theorems, are described extensively.