Fractals as Julia sets of a\exp[d\sin(z^n)]-bz + c via Jungck four-step iterative method with s -convexity as well as four-step iterative method

Fractals as Julia sets of a\exp[d\sin(z^n)]-bz + c


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Authors

  • Iqbal Ahmad Iqbal Qasim Univeristy
  • M. Sajid Qassim University, Saudi Arabia
  • R. Ahmad Aligarh Muslim University, Aligarh, India

Keywords:

Algorithms, Escape criteria, Julia sets, Fractals, Iterative methods, Convexity

Abstract

In this manuscript, we explore some new stunning fractals of Julia sets by developing the escape criteria for novel type of complex function $ p(z) = a \exp[d\sin(z^n)]- bz + c,$ where $n,|d|\geq 2$ and $a,b,c,d\in\mathbb{C}$ and furnish some graphical illustrations of the generated amazing fractals, utilizing the Jungck four-step iteration scheme equipped with $s$-convexity as well as four-step iteration scheme. Moreover, we conclude this work by examining variation in images and the impact of parameters on the deviation of dynamics, color, and appearance of fractals. At some fixed input parameters, we observe the engrossing behavior of Julia sets for different $n.$

Author Biographies

M. Sajid, Qassim University, Saudi Arabia

Full Professor, Department of Mechanical Engineering, College of Engineering, Qassim University.

R. Ahmad, Aligarh Muslim University, Aligarh, India

Full Professor, Department of Mathematics, AMU, Aligarh

References

(1) Mijanur Rahaman, Department of Mathematics, Syamaprasad College, Kolkata-700026, India

Email- mrahman96@yahoo.com

(2) Mohd Sarfaraz, Department of Mathematics, Jaypee Institute of Information Technology, Noida, India,

Email- sarfarazm820@gmail.com

(3) Vishnu Narayan Mishra, Applied Mathematics and Humanties Department, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat 395 007, India

Email-vishnunarayanmishra@gmail.com

(3) Vishnu Narayan Mishra, Applied Mathematics and Humanties Department, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat 395 007, India

Email-vishnunarayanmishra@gmail.com

(4) Chin-Tzong Pang, Department of Information Management, and Innovation Centre for Big Data and Digital Convergence, Yuan Ze University, Chung-Li 32003, Taiwan

Email: imctpang@saturn.yzu.edu.tw

(5) Ching-Feng Wen, Research Center for Nonliear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80708, Taiwan

Email: cfwen@kmu.edu.tw

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Published

2024-07-22

How to Cite

Iqbal, I. A., Sajid, M. S., & Rais, R. A. (2024). Fractals as Julia sets of a\exp[d\sin(z^n)]-bz + c via Jungck four-step iterative method with s -convexity as well as four-step iterative method: Fractals as Julia sets of a\exp[d\sin(z^n)]-bz + c. Results in Nonlinear Analysis, 7(3), 1–. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/387