The aim of this paper is to introduce the new concept of a multivalued Geraghty type contraction mapping using CG-simulation functions and C-class functions. Additionally, through this type of contraction, we establish fixed point results that generalize several known fixed point results in the literature. As consequences, we arrive at fixed point results endowed with graph. To demonstrate the credibility of our results, we give an example that proves it.

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.

In this manuscript, we introduce a new class of Colombeau algebras based on asymptotic almost automorphic functions and we prove some important properties of asymptotic almost automorphic generalized functions. We also illustrate all this in examples as an application.