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

Author

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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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