Fractal Functions and Fractal Dimensions on the Product of the Sierpiński Gaskets

被引：0
作者：
Jebali, Hajer [1 ]
机构：
[1] Univ Monastir, Fac Sci Monastir, Dept Math, Anal Probabil & Fractals Lab LR18ES17, Monastir 5000, Tunisia
来源：
RESULTS IN MATHEMATICS | 2025年 / 80卷 / 04期
关键词：
Fractal interpolation functions; Fractal dimension; Rakotch contractions; Sierpi & nacute; ski gasket; Invariant measure; Pluriharmonic functions; INTERPOLATION FUNCTIONS;
D O I：
10.1007/s00025-025-02425-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we construct a nonlinear fractal interpolation function on the product of the Sierpi & nacute;ski gaskets, and we prove that its graph is the unique attractor of an iterated function system defined, in a more general setting, by use of Rakotch contractions. Moreover, we use the H & ouml;lder continuity of pluriharmonic functions to estimate the fractal dimensions of the graph of the fractal interpolation function and those of the self-measure supported on it.
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页数：19
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