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Shape Preserving Aspects Of Bivariate α-Fractal Function

Author

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  • N. VIJENDER

    (Department of Mathematics, Visvesvaraya National Institute of Technology Nagpur, Nagpur 440010, India)

  • A. K. B. CHAND

    (Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India)

Abstract

In this paper, we study shape preserving aspects of bivariate α-fractal functions. Its specific aims are: (i) to solve the range restricted problem for bivariate fractal approximation (ii) to establish the fractal analogue of lionized Weierstrass theorem of bivariate functions (iii) to study the constrained approximation by 𠒞r-bivariate α-fractal functions (v) to investigate the conditions on the parameters of the iterated function system in order that the bivariate α-fractal function fα preserves fundamental shapes, namely, positivity and convexity (concavity) in addition to the smoothness of f over a rectangle (vi) to establish fractal versions of some elementary theorems in the shape preserving approximation of bivariate functions.

Suggested Citation

  • N. Vijender & A. K. B. Chand, 2021. "Shape Preserving Aspects Of Bivariate α-Fractal Function," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-13, November.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:07:n:s0218348x21501784
    DOI: 10.1142/S0218348X21501784
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    Cited by:

    1. Viswanathan, P., 2022. "A revisit to smoothness preserving fractal perturbation of a bivariate function: Self-Referential counterpart to bicubic splines," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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