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Fractal Dimension Of Multivariate α-Fractal Functions And Approximation Aspects

Author

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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)

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.

Suggested Citation

  • Megha Pandey & Vishal Agrawal & Tanmoy Som, 2022. "Fractal Dimension Of Multivariate α-Fractal Functions And Approximation Aspects," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-17, November.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:07:n:s0218348x22501493
    DOI: 10.1142/S0218348X22501493
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    Cited by:

    1. Verma, Manuj & Priyadarshi, Amit, 2023. "Graphs of continuous functions and fractal dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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