Common Attractor for Hutchinson θ-Contractive Operators in Partial Metric Spaces

Abstract

This paper investigates the existence of common attractors for generalized (Formula presented.) -Hutchinson operators within the framework of partial metric spaces. Utilizing a finite iterated function system composed of (Formula presented.) -contractive mappings, we establish theoretical results on common attractors, generalizing numerous existing results in the literature. Additionally, to enhance understanding, we present intuitive and easily comprehensible examples in one-, two-, and three-dimensional Euclidean spaces. These examples are accompanied by graphical representations of attractor images for various iterated function systems. As a practical application, we demonstrate how our findings contribute to solving a functional equation arising in a dynamical system, emphasizing the broader implications of the proposed approach.