Multivariate Zipper Fractal Functions

Abstract

AbstractA 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.KEYWORDS: Box dimensionfractal interpolation functionmonotonicitymultivariate Bernstein operatorpositivityzipperMATHEMATICS SUBJECT CLASSIFICATION: 28A8041A6341A0541A2941A3065D05 AcknowledgmentThe authors are thankful to the annonymous reviewers for their constructive suggestions to improve the presentation of the paper.