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Fractal generation via generalized Fibonacci–Mann iteration with s-convexity

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Abstract

Recently, the generalized Fibonacci–Mann iteration scheme has been defined and used to develop an escape criterion to study mutants of the classical fractals for a function \(\sin \left( z^{n}\right) +az+c\), \(a,c\in \mathbb {C}\), \(n\ge 2\), and z is a complex variable. In the current work, we use generalized Fibonacci–Mann iteration extended further via the notion of s-convex combination in the exploration of new mutants of celebrated Mandelbrot and Julia sets. Further, we provide a few graphical and numerical examples obtained by the use of the derived criteria.

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Acknowledgements

The authors are grateful to the anonymous referee for his precise remarks and suggestions which led to the improvement of this paper.

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Author notes

  1. N. Özgür and A. Tomar have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Army Cadet College Wing, Indian Military Academy, Dehradun, India

    Swati Antal

  2. Department of Mathematics, İzmir Democracy University, 35140, Karabağlar, İzmir, Turkey

    Nihal Özgür

  3. Department of Mathematics, Pt.L.M.S. Campus, Sridev Suman Uttarakhand University, Rishikesh, Uttarakhand, India

    Anita Tomar

  4. Institute of Computer Science, University of Silesia in Katowice, Bedzinska 39, 41-200, Sosnowiec, Poland

    Krzysztof Gdawiec

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  1. Swati Antal
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Correspondence to Swati Antal.

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Communicated by S.G. Dani.

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Antal, S., Özgür, N., Tomar, A. et al. Fractal generation via generalized Fibonacci–Mann iteration with s-convexity. Indian J Pure Appl Math (2024). https://doi.org/10.1007/s13226-024-00537-z

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