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

TL;DR

This paper introduces Proinov-type Z-contractions, a generalized form of contraction mappings using simulation functions, and demonstrates their fixed point properties and applications to fractal generation via iterated function systems.

Contribution

It generalizes Proinov-type contractions with simulation functions and establishes fixed point results in quasi-metric spaces, including applications to fractals.

Findings

Existence and uniqueness of fixed points for Proinov-type Z-contractions.

Construction of a new iterated function system with attractors.

Graphical examples illustrating the contraction mappings.

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.