Multivariate Zipper Fractal Functions

A novel approach to zipper fractal interpolation theory for functions of several variables is presented. Multivariate zipper fractal functions are constructed and then perturbed through free choices of base functions, scaling functions, and a binary matrix called signature to obtain their zipper α-f...

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Published inNumerical functional analysis and optimization Vol. 44; no. 14; pp. 1538 - 1569
Main Authors Kumar, D., Chand, A. K. B., Massopust, P. R.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 26.10.2023
Taylor & Francis Ltd
Subjects
Box dimension
fractal interpolation function
Fractals
Interpolation
Mathematical analysis
monotonicity
Multivariate analysis
multivariate Bernstein operator
positivity
Scaling factors
zipper
Online AccessGet full text
ISSN0163-0563
1532-2467
DOI10.1080/01630563.2023.2265722

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Abstract A novel approach to zipper fractal interpolation theory for functions of several variables is presented. Multivariate zipper fractal functions are constructed and then perturbed through free choices of base functions, scaling functions, and a binary matrix called signature to obtain their zipper α-fractal versions. In particular, we propose a multivariate Bernstein zipper fractal function and study its coordinate-wise monotonicity which depends on the values of signature. We derive bounds for the graph of a multivariate zipper fractal function by imposing conditions on the scaling factors and the Hölder exponent of the associated germ function and base function. The box dimension result for multivariate Bernstein zipper fractal function is derived. Finally, we study some constrained approximation properties for multivariate zipper Bernstein fractal functions.
AbstractList A novel approach to zipper fractal interpolation theory for functions of several variables is presented. Multivariate zipper fractal functions are constructed and then perturbed through free choices of base functions, scaling functions, and a binary matrix called signature to obtain their zipper α-fractal versions. In particular, we propose a multivariate Bernstein zipper fractal function and study its coordinate-wise monotonicity which depends on the values of signature. We derive bounds for the graph of a multivariate zipper fractal function by imposing conditions on the scaling factors and the Hölder exponent of the associated germ function and base function. The box dimension result for multivariate Bernstein zipper fractal function is derived. Finally, we study some constrained approximation properties for multivariate zipper Bernstein fractal functions.
Author Kumar, D.
Chand, A. K. B.
Massopust, P. R.
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  fullname: Chand, A. K. B.
  organization: Department of Mathematics, Indian Institute of Technology Madras
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  surname: Massopust
  fullname: Massopust, P. R.
  organization: School of Computation, Information and Technology, Department of Mathematics, Technical University of Munich (TUM)
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SubjectTerms Box dimension
fractal interpolation function
Fractals
Interpolation
Mathematical analysis
monotonicity
Multivariate analysis
multivariate Bernstein operator
positivity
Scaling factors
zipper
Title Multivariate Zipper Fractal Functions
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