FRACTAL DIMENSION OF MULTIVARIATE α-FRACTAL FUNCTIONS AND APPROXIMATION ASPECTS

Megha Pandey (), Vishal Agrawal and Tanmoy Som ()
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Megha Pandey: Department of Mathematical Sciences Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh 221005, India
Vishal Agrawal: Department of Mathematical Sciences Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh 221005, India
Tanmoy Som: Department of Mathematical Sciences Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh 221005, India

FRACTALS (fractals), 2022, vol. 30, issue 07, 1-17

Abstract: In this paper, we explore the concept of dimension preserving approximation of continuous multivariate functions defined on the domain [0, 1]q(= [0, 1] ×⋯ × [0, 1] (q-times) where q is a natural number). We establish a few well-known multivariate constrained approximation results in terms of dimension preserving approximants. In particular, we indicate the construction of multivariate dimension preserving approximants using the concept of α-fractal interpolation functions. We also prove the existence of one-sided approximation of multivariate function using fractal functions. Moreover, we provide an upper bound for the fractal dimension of the graph of the α-fractal function. Further, we study the approximation aspects of α-fractal functions and establish the existence of the Schauder basis consisting of multivariate fractal functions for the space of all real valued continuous functions defined on [0, 1]q and prove the existence of multivariate fractal polynomials for the approximation.

Keywords: Fractal Dimension; Fractal Interpolation; Fractal Surfaces; Bernstein Polynomials; Multivariate Constrained Approximation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501493

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