Some metrical $\varphi$-fixed point results of Wardowski type with applications to integral equations

Abstract

In this article, we define the concepts of $(\mathcal{F}^*,\varphi)$-contraction and $(\mathcal{F}^*,\varphi)$-expansion mappings in metric spaces and utilize the same to prove some $\varphi$-fixed point theorems for this kind of mappings. The obtained results used to present some results in partial metric spaces. Also, employing our newly results, we examine the existence and uniqueness of solution for integral equations. Furthermore supported example is provided.