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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Keywords:
Algorithms, Escape criteria, Julia sets, Fractals, Iterative methods, ConvexityAbstract
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 $n.$
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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