Equivalences of Ekeland-Type Variational Principle in the Setting of Quasi-Metric Spaces - Siawash, Syed Nasim (Journal of Natural Sciences – Kabul University, 2020)
In this paper, the concept of a Q-function defined on a quasi-metric space is introduced. This concept generalizes the notions of a τ-function and an ω-distance. We then present Ekeland-type variational principles within the context of quasi-metric spaces with a Q-function, followed by an equilibrium version of the Ekeland-type variational principle for complete quasi-metric spaces with a Q-function. The equivalence of these Ekeland-type variational principles with Caristi–Kirk type fixed point theorems for multivalued maps, the Takahashi minimization theorem, and some other related results in the setting of complete quasi-metric spaces with a Q-function are also stated and proven.