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<p>This paper presents a new class of operators, called <i>G</i>-norm enriched <i>F</i>-contractions, defined on <i>G</i>-Banach spaces. Using Krasnoselskii’s iteration method, we establish convergence results for the fixed points of these operators. These results are then applied to creating fractals related to the Hutchinson-Barnsley operator. To achieve this, we introduce a novel iterated function system (IFS), the <i>G</i>-norm IFS, which utilizes the properties of <i>G</i>-norm enriched <i>F</i>-contractions. Several examples demonstrate the convergence of the <i>G</i>-norm IFS to its attractor. Additionally, we show the existence and approximation of fractals generated by this construction, employing <i>G</i>-norm fractal interpolation functions. This application highlights the practical utility of our theoretical framework in generating and analyzing intricate fractal structures.</p>

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On G-Norm Hutchinson–Barnsley Operators and Their Convergence to Fractal Attractors

  • 期刊论文

  • 发表日期：

    2025年5月16日

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  • Hina Dilawer,
  • Hira Iqbal,
  • Rizwan Anjum

摘要

This paper presents a new class of operators, called G-norm enriched F-contractions, defined on G-Banach spaces. Using Krasnoselskii’s iteration method, we establish convergence results for the fixed points of these operators. These results are then applied to creating fractals related to the Hutchinson-Barnsley operator. To achieve this, we introduce a novel iterated function system (IFS), the G-norm IFS, which utilizes the properties of G-norm enriched F-contractions. Several examples demonstrate the convergence of the G-norm IFS to its attractor. Additionally, we show the existence and approximation of fractals generated by this construction, employing G-norm fractal interpolation functions. This application highlights the practical utility of our theoretical framework in generating and analyzing intricate fractal structures.