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On α-fractal functions and their applications to analyzing the S&P BSE Sensex in India

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  • Kumar, Anuj
  • Verma, Shubham Kumar
  • Boulaaras, Salah Mahmoud

Abstract

Following the seminal work of Barnsley on fractal interpolation, Navascués (2005) defined a class of parametrized continuous functions called α-fractal functions. In this paper, we construct α-fractal functions in the Lebesgue spaces defined with respect to a fractal measure. We also show the existence of these fractal functions in smooth-dimensional spaces. Further, we define some set-valued maps associated with them and study some properties of these maps. Ultimately, we analyze the S&P BSE Sensex in India with the help of α-fractal functions.

Suggested Citation

  • Kumar, Anuj & Verma, Shubham Kumar & Boulaaras, Salah Mahmoud, 2024. "On α-fractal functions and their applications to analyzing the S&P BSE Sensex in India," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s096007792400746x
    DOI: 10.1016/j.chaos.2024.115194
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    References listed on IDEAS

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    1. Păcurar, Cristina-Maria & Necula, Bogdan-Radu, 2020. "An analysis of COVID-19 spread based on fractal interpolation and fractal dimension," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Gupta, Deepika & Pandey, Asheesh, 2024. "Analyzing impact of corporate governance index on working capital management through fractal functions," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    3. Verma, Shubham Kumar & Kumar, Satish, 2024. "Fractal dimension analysis of financial performance of resulting companies after mergers and acquisitions," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    4. S. Verma & A. Sahu, 2022. "Bounded Variation On The Sierpiåƒski Gasket," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-12, November.
    5. Lal, Rattan & Chandra, Subhash & Prajapati, Ajay, 2024. "Fractal surfaces in Lebesgue spaces with respect to fractal measures and associated fractal operators," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    6. Subhash Chandra & Syed Abbas, 2021. "The Calculus Of Bivariate Fractal Interpolation Surfaces," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-13, May.
    7. Yu, Binyan & Liang, Yongshun, 2024. "On the dimensional connection between a class of real number sequences and local fractal functions with a single unbounded variation point," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    8. Binyan Yu & Yongshun Liang, 2024. "Research On Fractal Dimensions And The Hã–Lder Continuity Of Fractal Functions Under Operations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-28.
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