SHAPE PRESERVING ASPECTS OF BIVARIATE α-FRACTAL FUNCTION

N. Vijender and A. K. B. Chand ()
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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

FRACTALS (fractals), 2021, vol. 29, issue 07, 1-13

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.

Keywords: Fractals; Iterated Function Systems; Bivariate α-Fractal Function; Constrained Fractal Approximation; Range Restricted Fractal Approximation; Positivity; Convexity (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501784

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