Generalized Proinov-type contractions using simulation functions with applications to fractals

Abstract

The intention of this article is to introduce a generalization of Proinov-type contraction via simulation functions. We name this generalized contraction map as Proinov-type Z-contraction. This article establishes the existence and uniqueness of fixed points for these contraction mappings in quasi-metric space and also, include explanatory examples with graphical interpretation. As an application, we generate a new iterated function system (IFS) consisting of Proinov-type Z-contractions in quasi-metric spaces. At the end of the paper, we prove the existence of a unique attractor for the IFS consisting of Proinov-type Z-contractions.