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Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 16
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Articles

Approximation properties of bivariate α-fractal functions and dimension results

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Pages 3426-3444 | Received 03 Jun 2019, Accepted 21 Jan 2020, Published online: 02 Feb 2020
 

ABSTRACT

In this paper, we study a different class of bivariate α-fractal functions. First, we introduce the bivariate Bernstein α-fractal functions that are more suitable to approximate both smooth and non-smooth surfaces and investigate their convergence properties. Then, we compute the box-counting dimension of the graph of the bivariate α-fractal functions for equally spaced data set. In regard to the connection of functional analysis and fractal function, we cogitate the bivariate fractal operator in spaces of functions such as k-times continuously differentiable functions space Ck(I×J) and the Lebesgue space Lp(I×J). Also, we study some approximation properties using bivariate Bernstein α-fractal trigonometric functions.

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Acknowledgments

We thank the anonymous reviewers for the valuable and constructive suggestions that helped to improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

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