Fractals in $$S_b$$ -metric spaces

Abstract

This study aims to discover attractors for fractals by using generalized F-contractive iterated function system, which falls within a distinct category of mappings defined on \(S_b\)-metric spaces. In particular, we investigate how these systems, when subjected to specific F-contractive conditions, can lead to the identification of a unique attractor. We achieve a diverse range of outcomes for iterated function systems that adhere to a unique set of generalized F-contractive conditions. Our approach includes a detailed theoretical framework that establishes the existence and uniqueness of attractors in these settings. We provide illustrative examples to bolster the findings established in this work and use the functions given in the example to construct fractals and discuss the convergence of the obtained fractals via iterated function system to an attractor. These examples demonstrate the practical application of our theoretical results, showcasing the convergence behavior of fractals generated by our proposed systems. These outcomes extend beyond the scope of various existing results found in the current body of literature. By expanding the applicability of F-contractive conditions, our findings contribute to the broader understanding of fractal geometry and its applications, offering new insights and potential directions for future research in this area.