Generalized G-Hausdorff space and applications in fractals

Abstract

In this paper, we introduce the concept of a G-Hausdorff space and show how the results established in the usual metric space can be generalized to the G-metric space. The proven results are used to propose an iterated function system (IFS) called G-IFS. Additionally, the existence of the fractal associated with this construction is demonstrated. This paper shows how non-affine transformations and fractal interpolation functions (FIFs) can be used to approximate fractals by G-IFS. This paper contributes to the understanding of fractal geometry and its applications in mathematics and other fields.