New Type of Fractal Functions for the General Data Sets

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Acta Applicandae Mathematicae Pub Date : 2023-09-25 DOI:10.1007/s10440-023-00604-3

Manuj Verma, Amit Priyadarshi

引用次数: 0

Abstract

In this paper, we prove the existence of the fractal interpolation function corresponding to a general data set using the Rakotch contraction theory and iterated function system. We also prove the existence of the fractal measure supported on the graph of the fractal interpolation function. We emphasize the fact that our theory covers the fractal interpolation theory for finite cases, countably infinite cases, and many more. We establish dimensional results for the graph of the fractal interpolation function for the general data sets.

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一般数据集的新型分形函数

本文利用Rakoch收缩理论和迭代函数系统，证明了一般数据集对应的分形插值函数的存在性。我们还证明了分形插值函数图上支持的分形测度的存在性。我们强调，我们的理论涵盖了有限情况、可数无限情况以及更多情况下的分形插值理论。我们建立了一般数据集的分形插值函数图的维数结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Applicandae Mathematicae 数学-应用数学

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

16.2 months

期刊介绍： Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.