Multivariate Zipper Fractal Functions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-12 DOI:10.1080/01630563.2023.2265722

D. Kumar, A. K. B. Chand, P. R. Massopust

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引用次数: 0

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.

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多元拉链分形函数

摘要提出了一种多变量函数的拉链分形插值理论的新方法。构造多元拉链分形函数，并通过自由选择基函数、标度函数和一个称为signature的二元矩阵对其进行扰动，得到它们的拉链α-分形版本。特别地，我们提出了一个多元Bernstein拉链分形函数，并研究了它依赖于签名值的坐标单调性。通过对尺度因子和相关胚芽函数和基函数的Hölder指数施加条件，导出了多元拉链分形函数图的界。导出了多元Bernstein拉链分形函数的箱维结果。最后，研究了多元zippers Bernstein分形函数的约束近似性质。关键词:盒维数分形插值函数单调性多元Bernstein算子正性zipper数学主题分类:28A8041A6341A0541A2941A3065D05致谢感谢匿名审稿人为改进本文的表述提出的建设性建议。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.