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Article

On the Bernstein Affine Fractal Interpolation Curved Lines and Surfaces

1
Department of Mathematics, Visvesvaraya National Institute of Technology Nagpur, Nagpur 440006, India
2
Department of Computer Science and Biomedical Informatics, University of Thessaly, 35131 Lamia, Greece
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Axioms 2020, 9(4), 119; https://doi.org/10.3390/axioms9040119
Received: 31 August 2020 / Revised: 8 October 2020 / Accepted: 9 October 2020 / Published: 18 October 2020
(This article belongs to the Special Issue Fractional Calculus, Wavelets and Fractals)
In this article, firstly, an overview of affine fractal interpolation functions using a suitable iterated function system is presented and, secondly, the construction of Bernstein affine fractal interpolation functions in two and three dimensions is introduced. Moreover, the convergence of the proposed Bernstein affine fractal interpolation functions towards the data generating function does not require any condition on the scaling factors. Consequently, the proposed Bernstein affine fractal interpolation functions possess irregularity at any stage of convergence towards the data generating function. View Full-Text
Keywords: attractor; Bernstein polynomial; bivariate surfaces; dynamic system; fractal interpolation; iterated function system attractor; Bernstein polynomial; bivariate surfaces; dynamic system; fractal interpolation; iterated function system
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MDPI and ACS Style

Vijender, N.; Drakopoulos, V. On the Bernstein Affine Fractal Interpolation Curved Lines and Surfaces. Axioms 2020, 9, 119. https://doi.org/10.3390/axioms9040119

AMA Style

Vijender N, Drakopoulos V. On the Bernstein Affine Fractal Interpolation Curved Lines and Surfaces. Axioms. 2020; 9(4):119. https://doi.org/10.3390/axioms9040119

Chicago/Turabian Style

Vijender, Nallapu, and Vasileios Drakopoulos. 2020. "On the Bernstein Affine Fractal Interpolation Curved Lines and Surfaces" Axioms 9, no. 4: 119. https://doi.org/10.3390/axioms9040119

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