On Multivalued Fuzzy Contractions in Extended b -Metric Spaces

Abstract

In this paper, we establish a Hausdorff metric over the family of nonempty closed subsets of an extended $b$ -metric space. Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related $\alpha$ -fuzzy fixed point theorems in the context of extended $b$ -metric spaces that generalize Nadler’s fixed point theorem as well as many preexisting results in the literature. Further, we establish $\alpha$ -fuzzy fixed point theorems for Ćirić type fuzzy contraction mappings as a generalization of previous results. Moreover, we give some examples to support the obtained results.