CONSTRUCTION OF MONOTONOUS APPROXIMATION BY FRACTAL INTERPOLATION FUNCTIONS AND FRACTAL DIMENSIONS

被引：5
|
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
收藏
页数：15
相关论文
共 50 条
  • [41] Zipper rational fractal interpolation functions
    Pasupathi, R.
    Vijay
    Chand, A. K. B.
    Upadhye, N. S.
    JOURNAL OF ANALYSIS, 2024, 32 (06): : 3197 - 3226
  • [42] Affine recurrent fractal interpolation functions
    Balasubramani, N.
    Gowrisankar, A.
    EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2021, 230 (21-22): : 3765 - 3779
  • [43] Univariable affine fractal interpolation functions
    Drakopoulos, V.
    Vijender, N.
    THEORETICAL AND MATHEMATICAL PHYSICS, 2021, 207 (03) : 689 - 700
  • [44] On the integral transform of fractal interpolation functions
    Agathiyan, A.
    Gowrisankar, A.
    Fataf, Nur Aisyah Abdul
    MATHEMATICS AND COMPUTERS IN SIMULATION, 2024, 222 : 209 - 224
  • [45] Multifractal analysis of fractal interpolation functions
    Priyanka, T. M. C.
    Gowrisankar, A.
    PHYSICA SCRIPTA, 2024, 99 (11)
  • [46] Energy and Laplacian of fractal interpolation functions
    Li Xiao-hui
    Ruan Huo-jun
    APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B, 2017, 32 (02) : 201 - 210
  • [47] Bivariate fractal interpolation functions on grids
    Dalla, L
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2002, 10 (01) : 53 - 58
  • [48] The　Smoothnes　and　Dimension　of　Fractal　Interpolation　Functions
    Chen Gang
    Applied Mathematics:A Journal of Chinese Universities(Series B), 1996, (04) : 35 - 44
  • [49] Energy and Laplacian of fractal interpolation functions
    Xiao-hui Li
    Huo-jun Ruan
    Applied Mathematics-A Journal of Chinese Universities, 2017, 32 : 201 - 210
  • [50] Wavelets are piecewise fractal interpolation functions
    Hardin, DP
    FRACTALS IN MULTIMEDIA, 2002, 132 : 121 - 135
12345