Generalized G-Hausdorff space and applications in fractals

Kifayat Ullah and S.K. Katiyar

Chaos, Solitons & Fractals, 2023, vol. 174, issue C

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.

Keywords: Completeness; Fixed point; Hausdorff metric; Iterated function system; Fractals; Fractal interpolation function; Affine map (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007208

DOI: 10.1016/j.chaos.2023.113819

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