Fixed point theorem for a new SF-GF-contraction mappings in metric space with supportive applications

Abstract

This manuscript has for goal to present a new type of contraction, namely SF -GF -contraction, based on the simulation function and the Geraghty function. Some existence and uniqueness results of fixed point in complete metric spaces have been shown with this contraction. Our results generalize and unify several existing results in the literature. Moreover, we illustrated these results with some examples and applications.