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<p>In this paper, we construct a nonlinear fractal interpolation function on the product of the Sierpiński 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 Hölder 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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年5月20日

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  • Hajer Jebali

摘要

In this paper, we construct a nonlinear fractal interpolation function on the product of the Sierpiński 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 Hölder 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.