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Generalized G-Hausdorff space and applications in fractals

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  • Ullah, Kifayat
  • Katiyar, S.K.

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.

Suggested Citation

  • Ullah, Kifayat & Katiyar, S.K., 2023. "Generalized G-Hausdorff space and applications in fractals," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007208
    DOI: 10.1016/j.chaos.2023.113819
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    References listed on IDEAS

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    1. Llorens-Fuster, Enrique & Petruşel, Adrian & Yao, Jen-Chih, 2009. "Iterated function systems and well-posedness," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1561-1568.
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    Full references (including those not matched with items on IDEAS)

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