An iteration process for a general class of contractive-like operators: Convergence, stability and polynomiography

Ti-Ming Yu; Abdul Aziz Shahid; Khurram Shabbir; Nehad Ali Shah; Yong-Min Li; Ti-Ming Yu; Abdul Aziz Shahid; Khurram Shabbir; Nehad Ali Shah; Yong-Min Li

doi:10.3934/math.2021393

AIMS Mathematics

2021, Volume 6, Issue 7: 6699-6714. doi: 10.3934/math.2021393

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An iteration process for a general class of contractive-like operators: Convergence, stability and polynomiography

1.
School of Economic Information Engineering, Southwestern University of Finance and Economics, Chengdu 611130, China
2.
Department of Mathematics and Statistics, University of Lahore, Lahore 54000, Pakistan
3.
Department of Mathematics, GC University, Lahore 54000, Pakistan
4.
Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
5.
Department of Mathematics, Lahore Leads University, Lahore, Pakistan
6.
Department of Mathematics, Huzhou University, Huzhou 313000, China

Received: 26 December 2020 Accepted: 31 March 2021 Published: 19 April 2021
MSC : 34N05, 35A23

In this paper, we propose a three step iteration process and analyze the performance of the process for a contractive-like operators. It is observed that this iterative procedure is faster than several iterative methods in the existing literature. To support the claim, a numerical example is presented using Maple 13. Some images are generated by using this iteration method for complex cubic polynomials. We believe that our presented work enrich the polynomiography software.
- iterative schemes,
- image generation,
- contractive-like operators,
- convergence,
- polynomials
Citation: Ti-Ming Yu, Abdul Aziz Shahid, Khurram Shabbir, Nehad Ali Shah, Yong-Min Li. An iteration process for a general class of contractive-like operators: Convergence, stability and polynomiography[J]. AIMS Mathematics, 2021, 6(7): 6699-6714. doi: 10.3934/math.2021393

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Abstract

In this paper, we propose a three step iteration process and analyze the performance of the process for a contractive-like operators. It is observed that this iterative procedure is faster than several iterative methods in the existing literature. To support the claim, a numerical example is presented using Maple 13. Some images are generated by using this iteration method for complex cubic polynomials. We believe that our presented work enrich the polynomiography software.

References

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