Kaleva-Seikkala’s Type Fuzzy b-Metric Spaces and Several Contraction Mappings

Abstract

In this paper, we introduce the concept of Kaleva-Seikkala’s type fuzzy b-metric spaces as a generalization of the notion of b-metric spaces and fuzzy metric spaces. In such spaces, we establish Banach type, Reich type, and Chatterjea type fixed-point theorems, which improve the relevant results in fuzzy metric spaces. Two technical lemmas are employed to ensure that a Picard sequence is a Cauchy sequence. Finally, various applications are given to testify the fact that our main theorems extend the cases of b-metric spaces.