FRACTAL DIMENSION OF PRODUCT OF CONTINUOUS FUNCTIONS WITH BOX DIMENSION

被引：2

作者：

Liu, Peizhi ^{[1
]}

DU, Yumeng ^{[1
]}

Liang, Yongshun ^{[1
]}

机构：

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

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2023年 / 31卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Fractal Functions; Fractal Dimension; Product of Continuous Functions; GRAPHS;

D O I：

10.1142/S0218348X23500214

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper investigates fractal dimension of product of continuous functions with Box dimension on [0, 1]. For two continuous functions with different Box dimensions, the Box dimension of their product has been proved to be the larger one. Furthermore, the Box dimension of product of two continuous functions with the same Box dimension may not exist. Definitions of regular fractal and local fractal functions have been given. Product of a regular fractal function and a local fractal function with the same Box dimension must still be the original Box dimension.

引用

页数：8

共 50 条

[1] SOME RESULTS ON BOX DIMENSION ESTIMATION OF FRACTAL CONTINUOUS FUNCTIONS
Yang, Huai
Ren, Lulu
Zheng, Qian
[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2024, 32 (03)
[2] Box dimension for graphs of fractal functions
Brown, G
Yin, QH
[J]. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1997, 40 : 331 - 344
[3] FRACTAL DIMENSIONS OF LINEAR COMBINATION OF CONTINUOUS FUNCTIONS WITH THE SAME BOX DIMENSION
Wang, Xuefei
Zhao, Chunxia
[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2020, 28 (07)
[4] Fractal Dimension of Fractional Integral of Continuous Functions
Du, Junhuai
Xiao, Wei
Liang, Yongshun
[J]. 2017 29TH CHINESE CONTROL AND DECISION CONFERENCE (CCDC), 2017, : 7838 - 7844
[5] ON THE BOX DIMENSION FOR A CLASS OF NONAFFINE FRACTAL INTERPOLATION FUNCTIONS
L.Dalla
V.Drakopoulos
M.Prodromou
[J]. Analysis in Theory and Applications, 2003, (03) : 220 - 233
[6] Box Dimension and Fractional Integrals of Multivariate α-Fractal Functions
Agrawal, Vishal
Pandey, Megha
Som, Tanmoy
[J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2023, 20 (03)
[7] Box dimension of generalized affine fractal interpolation functions
Jiang, Lai
Ruan, Huo-Jun
[J]. JOURNAL OF FRACTAL GEOMETRY, 2023, 10 (3-4) : 279 - 302
[8] On a class of fractal functions with graph Box dimension 2
Xie, TF
Zhou, SP
[J]. CHAOS SOLITONS & FRACTALS, 2004, 22 (01) : 135 - 139
[9] Fractal Dimension of Graphs of Typical Continuous Functions on Manifolds
Mirzaie, Reza
[J]. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS, 2018, 13 (02): : 93 - 99
[10] FRACTAL DIMENSION OF CERTAIN CONTINUOUS FUNCTIONS OF UNBOUNDED VARIATION
Liang, Y. S.
Su, W. Y.
[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2017, 25 (01)

← 1 2 3 4 5 →