Caristi's fixed point theorem, Ekeland's variational principle and Takahashi's maximization theorem in fuzzy quasi-metric spaces

Abstract

In this paper, a partial order and its basic properties are exploited in a fuzzy quasi-metric space in the sense of George and Veeramani (1994) [17]. Based on this partial order, Caristi's fixed point theorem, Ekeland's variational principle and Takahashi's maximization theorem are extended to fuzzy quasi-metric spaces by using the Brézis and Browder principle on ordered sets. Moreover, an equivalence chain among these theorems is provided.