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<p>A novel class of iterated function systems (IFSs) based on Pata-type contractions is introduced, extending traditional IFSs defined by Banach contractions. The existence of attractors for these systems is established. Leveraging this framework, new methods for constructing fractal interpolation functions (FIFs) are developed, broadening the possibilities for fractal interpolation. The illustrative examples demonstrate the application of these IFSs in generating FIFs.</p>

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Nonlinear iterated function systems and fractal interpolation functions with Pata-type contractions

  • 期刊论文

  • 发表日期：

    2025年8月21日

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  • Zhong Dai,
  • Shutang Liu

摘要

A novel class of iterated function systems (IFSs) based on Pata-type contractions is introduced, extending traditional IFSs defined by Banach contractions. The existence of attractors for these systems is established. Leveraging this framework, new methods for constructing fractal interpolation functions (FIFs) are developed, broadening the possibilities for fractal interpolation. The illustrative examples demonstrate the application of these IFSs in generating FIFs.