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

Anuj Kumar, Shubham Kumar Verma and Salah Mahmoud Boulaaras

Chaos, Solitons & Fractals, 2024, vol. 186, issue C

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.

Keywords: Fractal interpolation; IFS; α-fractal function; Box dimension; Approximation; Sensex; Pattern recognition (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:186:y:2024:i:c:s096007792400746x

DOI: 10.1016/j.chaos.2024.115194

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