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<p>In this paper, we develop the proximal iterated function systems <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13663_2025_784_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="61" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mi>P</mi> <mi>I</mi> <mi>F</mi> <mi>S</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$(PIFS)$</EquationSource> </InlineEquation> using cyclic Meir-Keeler contractions and hence give an application in the fractal theory by constructing fractals using the new <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13663_2025_784_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>I</mi> <mi>F</mi> <mi>S</mi> </math></EquationSource> <EquationSource Format="TEX">$IFS$</EquationSource> </InlineEquation>. Furthermore, we extend the results to countable <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13663_2025_784_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>P</mi> <mi>I</mi> <mi>F</mi> <mi>S</mi> </math></EquationSource> <EquationSource Format="TEX">$PIFS$</EquationSource> </InlineEquation>.</p>

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Proximal iterated function systems using cyclic Meir-Keeler contractions and an application to fractal theory

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月25日

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  • A. Sreelakshmi Unni,
  • V. Pragadeeswarar

摘要

In this paper, we develop the proximal iterated function systems ( P I F S ) $(PIFS)$ using cyclic Meir-Keeler contractions and hence give an application in the fractal theory by constructing fractals using the new I F S $IFS$ . Furthermore, we extend the results to countable P I F S $PIFS$ .