Comparison Function and Boyd–Wong–Type Contractions in Kaleva–Seikkala’s Type Fuzzy b-Metric Space

Abstract

In this article, we study the existence and uniqueness of fixed points for mappings in Kaleva–Seikkala’s type fuzzy b-metric spaces. Nonlinear contractions of the comparison function and Boyd–Wong’s type are considered, and several new fixed point theorems for these contractions in complete Kaleva-Seikkala’s type fuzzy b-metric spaces are presented. It is remarkable that the contractive conditions of our results do not depend on the space coefficient b. The presented work extends and improves some well-known results in the literature. Finally, as an application, we demonstrate a unique solution to both the Fredholm integral equation and the fractional differential equation.