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<p>In this paper, a simple series representation of fractal interpolation functions (FIFs) is established. We first construct a series representation for the Laplace transform of FIFs. Then, by the uniqueness property of the Laplace transform, FIFs in a specific case can be expressed as a simple series. Such a series form shows a more explicit connection between FIFs and Weierstrass-type functions. According to this connection, some known results about the fractal dimension of the graph of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13540_2025_443_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(W_{\phi }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>W</mi> <mi>ϕ</mi> </msub> </math></EquationSource> </InlineEquation> can be applied to obtain the fractal dimension of the graph of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13540_2025_443_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(f_{[u]}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>f</mi> <mrow> <mo stretchy="false">[</mo> <mi>u</mi> <mo stretchy="false">]</mo> </mrow> </msub> </math></EquationSource> </InlineEquation>, and vice versa. We discuss some cases in our paper.</p>

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A simple series representation for a class of fractal interpolation functions

  • 期刊论文

  • 发表日期：

    2025年9月12日

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  • Dah-Chin Luor,
  • Chiao-Wen Liu

摘要

In this paper, a simple series representation of fractal interpolation functions (FIFs) is established. We first construct a series representation for the Laplace transform of FIFs. Then, by the uniqueness property of the Laplace transform, FIFs in a specific case can be expressed as a simple series. Such a series form shows a more explicit connection between FIFs and Weierstrass-type functions. According to this connection, some known results about the fractal dimension of the graph of \(W_{\phi }\) W ϕ can be applied to obtain the fractal dimension of the graph of \(f_{[u]}\) f [ u ] , and vice versa. We discuss some cases in our paper.