Dimensional Analysis of α-Fractal Functions

被引：0

作者：

Jha, S. ^{[1
]}

Verma, S. ^{[2
]}

机构：

[1] NIT Rourkela, Dept Math, Rourkela 769008, India

[2] IIIT Allahabad, Dept Appl Sci, Allahabad 211015, Uttar Pradesh, India

来源：

RESULTS IN MATHEMATICS | 2021年 / 76卷 / 04期

关键词：

Iterated function systems; fractal interpolation functions; Hausdorff dimension; box dimension; open set condition; SEPARATION PROPERTIES; INTERPOLATION;

D O I：

10.1007/s00025-021-01495-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide a rigorous study on dimensions of fractal interpolation functions defined on a closed and bounded interval of R which are associated to a continuous function with respect to a base function, scaling functions and a partition of the interval. In particular, we calculate an exact estimation of box dimension of alpha-fractal functions under suitable hypotheses on the iterated function system.

引用

页数：24

共 50 条

[41] Fractal functions on the sphere
Navascues, M. A.
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2007, 9 (03) : 257 - 270
[42] Fractal Convolution: A New Operation Between Functions
María A. Navascués
Peter R. Massopust
Fractional Calculus and Applied Analysis, 2019, 22 : 619 - 643
[43] FRACTAL CONVOLUTION: A NEW OPERATION BETWEEN FUNCTIONS
Navascues, Maria A.
Massopust, Peter R.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2019, 22 (03) : 619 - 643
[44] Fractal Functions and Fractal Dimensions on the Product of the Sierpiński GasketsFractal Functions and Fractal DimensionsH. Jebali
Hajer Jebali
Results in Mathematics, 2025, 80 (4)
[45] Katugampola Fractional Integral and Fractal Dimension of Bivariate Functions
S. Verma
P. Viswanathan
Results in Mathematics, 2021, 76
[46] Cubic Hermite and Cubic Spline Fractal Interpolation Functions
Chand, A. K. B.
Viswanathan, P.
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2012), VOLS A AND B, 2012, 1479 : 1467 - 1470
[47] Katugampola Fractional Integral and Fractal Dimension of Bivariate Functions
Verma, S.
Viswanathan, P.
RESULTS IN MATHEMATICS, 2021, 76 (04)
[48] Fractal interpolation functions with variable parameters and their analytical properties
Wang, Hong-Yong
Yu, Jia-Shan
JOURNAL OF APPROXIMATION THEORY, 2013, 175 : 1 - 18
[49] CARDINALITY AND FRACTAL LINEAR SUBSPACE ABOUT FRACTAL FUNCTIONS
Xiao, Wei
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2022, 30 (07)
[50] A note on stability and fractal dimension of bivariate α-fractal functions
V. Agrawal
T. Som
S. Verma
Numerical Algorithms, 2023, 93 : 1811 - 1833

← 1 2 3 4 5 →