On multivalued fuzzy contractions in extended \(b\)-metric spaces (Q2034600)

Summary: 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.