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<p>Based on Geraghty contractions, we construct a generalized class of nonlinear fractal interpolation functions on the Sierpiński gasket and we investigate some of their properties. We prove that the graphs of these functions are attractors of certain iterated function systems. Additionally, we estimate the fractal dimensions of the graph of the fractal interpolation function and the Hewitt–Stromberg dimension of the invariant measure supported on it.</p>

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Fractal functions, self-similar measure and fractal dimensions on the Sierpiński gasket

  • 期刊论文

  • 发表日期：

    2025年10月13日

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  • Hajer Jebali,
  • Alireza Khalili Golmankhaneh

摘要

Based on Geraghty contractions, we construct a generalized class of nonlinear fractal interpolation functions on the Sierpiński gasket and we investigate some of their properties. We prove that the graphs of these functions are attractors of certain iterated function systems. Additionally, we estimate the fractal dimensions of the graph of the fractal interpolation function and the Hewitt–Stromberg dimension of the invariant measure supported on it.