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We develop the escape criterion for higher-order complex-valued polynomials \(f(z)=z^n+az^2+bz+c\) via three-step Noor iteration endowed with s-convexity. From this, we deduce the escape criterion for the same polynomial using Ishikawa and Mann iterations endowed with s-convexity. We use our results to explore mutants of the classical Mandelbrot as well as Julia sets in Noor, Ishikawa and Mann orbits endowed with s-convexity and observe certain patterns in these distinct orbits. It is interesting that most of the visualized fractals have a ring in the center and are similar to beautiful natural objects.

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Application of Fixed Point Iterations in Generation of Fractals for Higher-Order Complex Polynomial

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  • 发表日期：

    2025年

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  • Shivam Rawat,
  • Darshana J. Prajapati,
  • Anita Tomar,
  • R. C. Dimri

摘要

We develop the escape criterion for higher-order complex-valued polynomials \(f(z)=z^n+az^2+bz+c\) via three-step Noor iteration endowed with s-convexity. From this, we deduce the escape criterion for the same polynomial using Ishikawa and Mann iterations endowed with s-convexity. We use our results to explore mutants of the classical Mandelbrot as well as Julia sets in Noor, Ishikawa and Mann orbits endowed with s-convexity and observe certain patterns in these distinct orbits. It is interesting that most of the visualized fractals have a ring in the center and are similar to beautiful natural objects.