Ekeland's variational principle in fuzzy quasi-normed spaces

Abstract

Fuzzy quasi-normed space provides an ideal mathematical framework for studying asymmetric phenomena. In this paper, we prove a version of the Ekeland variational principle in fuzzy quasi-normed spaces and apply it to Caristi's fixed point theorem and Takahashi minimization theorem. Moreover, we prove the equivalence relations among these theorems.

Keywords

• fuzzy quasi-norm
• variational principle
• fixed point theorem
• minimization theorem