CONSTRUCTION OF MONOTONOUS APPROXIMATION BY FRACTAL INTERPOLATION FUNCTIONS AND FRACTAL DIMENSIONS

被引：7

作者：

Yu, Binyan ^{[1
]}

Liang, Yongshun ^{[1
]}

机构：

[1] Nanjing Univ Sci & Technol, Sch Math & Stat, Nanjing 210094, Peoples R China

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2024年 / 32卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Monotonous Approximation; Fractal Interpolation Functions; The Hausdorff Dimension; The Box Dimension; Self-Affine Functions; Variation; PARAMETER-IDENTIFICATION PROBLEM; BOX DIMENSION;

D O I：

10.1142/S0218348X24400061

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we research on the dimension preserving monotonous approximation by using fractal interpolation techniques. A constructive result of the approximating sequence of self-affine continuous functions has been given, which can converge to the object continuous function of bounded variation on [0, 1] monotonously and unanimously, meanwhile their graphs can be any value of the Hausdorff and the Box dimension between one and two. Further, such approximation for continuous functions of unbounded variation or even general continuous functions with non-integer fractal dimension has also been discussed elementarily.

引用

页数：15

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