On fixed point results in a new type of nonlinear contraction in $\mathfrak{b}$-metric spaces with applications to differential equations

Abstract

We present fixed point theorem for a new type of nonlinear contractive mappings in $\mathfrak{b}$-metric spaces. Also, we present examples to illustrate the validity of the results obtained in the paper. In addition, by using our results, we obtain the existence and uniqueness of solution to some ordinary differential equations with initial value conditions.