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Boundaries of Filled Julia sets in Generalized Jungck Mann Orbit

Dong li, Muhammad Tanveer, Waqas Nazeer, Xiaorui Guo
2019 IEEE Access  
In this paper, we study the generalized Jungck Mann orbit (GJMO) and prove the converse theorem of results.  ...  We develop algorithms for the generation of filled Julia sets and their boundaries in the GJMO.  ...  Recently, Kwun et al. presented some Mandelrot sets, Julia sets and Biomorphs in Jungck-CR orbit with s-convexity [16] and in modified Jungck-S orbit [17] respectively.  ... 
doi:10.1109/access.2019.2920026 fatcat:uc5c4hehvzg63cdnm6mb7q7uia

Dynamics of antifractals in modified S-iteration orbit

Zhihua Chen, Abdul Aziz Shahid, Tariq Javed Zia, Imran Ahmed, Waqas Nazeer
2019 IEEE Access  
The aim of this paper is to visualize antifractals like tricorns and multicorns in S-iteration orbit with s-convexity.  ...  INDEX TERMS S-iteration, s-convexity, anti-Julia set, tricorn, escape criterion. This work is licensed under a Creative Commons Attribution 4.0 License.  ...  Chen et al.: Dynamics of Antifractals in Modified S-Iteration Orbit FIGURE 1 . 1 Tricorn generated in S-iteration orbit with s-convexity.  ... 
doi:10.1109/access.2019.2934748 fatcat:ulcclycfhzcyhnlclvpwh5s6oy

Tricorns and Multicorns in Noor orbit with s-convexity

Young Chel Kwun, Abdul Aziz Shahid, Waqas Nazeer, Saad I. Butt, Mujahid Abbas, Shin Min Kang
2019 IEEE Access  
Various patterns are displayed to investigate the geometry of antifractals for antipolynomial z k+1 + c of complex polynomial z k+1 + c, for k ≥ 1 in Noor orbit with s-convexity.  ...  In today's world, complex patterns of the dynamical framework have astounding highlights of fractals and become a huge field of research because of their beauty and unpredictability of their structure.  ...  [16] handled the Jungck-Mann and Jungck-Ishikawa iteration procedures and Kang et al. [17] presented new fixed point results for formation of fractals with s-convexity in Jungck-Noor orbit.  ... 
doi:10.1109/access.2019.2928796 fatcat:lgrb2q5libdpzofxl2iwr632pq

Generation of Julia and Madelbrot Sets via Fixed Points

Mujahid Abbas, Hira Iqbal, Manuel De la Sen
2020 Symmetry  
The aim of this paper is to present an application of a fixed point iterative process in generation of fractals namely Julia and Mandelbrot sets for the complex polynomials of the form T ( x ) = x n +  ...  We prove some escape time results for the generation of Julia and Madelbrot sets using a Picard Ishikawa type iterative process.  ...  [28] introduced Julia and Mandelbrot sets in implicit Jungck Mann and Jungck Ishikawa orbits.  ... 
doi:10.3390/sym12010086 fatcat:6ycq6xwbzfejxfu7us5ewzrid4

Fixed point results for the complex fractal generation in the S -iteration orbit with s -convexity

Krzysztof Gdawiec, Abdul Aziz Shahid
2018 Open Journal of Mathematical Sciences  
In this paper we introduce in the generation process of Mandelbrot and Julia sets a combination of the S-iteration, known from the fixed point theory, and the s-convex combination.  ...  We derive the escape criteria needed in the generation process of those fractals and present some graphical examples. Mathematics Subject Classification :37F45, 37F50, 47J25  ...  In [20] Kang et al. introduced new fixed point results for fractal generation using the implicit Jungck-Noor orbit with s-convexity, whereas Nazeer et al. in [21] used the Jungck-Mann and Jungck-Ishikawa  ... 
doi:10.30538/oms2018.0017 fatcat:l7d6p7aitzdu5ohwbzkzyrn3p4

Fractal generation via CR iteration scheme with s-convexity

Young Chel Kwun, Abdul Aziz Shahid, Waqas Nazeer, Mujahid Abbas, Shin Min Kang
2019 IEEE Access  
The aim of this paper is to provide escape criterion and generate fractals (Julia sets and Mandelbrot sets) via CR iteration scheme with s-convexity.  ...  One can find many generalizations of these sets in the literature. One such generalization is the use of results from fixed-point theory.  ...  [24] , [25] generated fractals via Jungck-CR and Modified Jungck-S iterations with sconvexity.  ... 
doi:10.1109/access.2019.2919520 fatcat:nzomq5u45baxjjy7krloo4gnza

CR iteration in generation of antifractals with s-convexity

Dong Li, Abdul Aziz Shahid, Asifa Tassaddiq, Arshad Khan, Xiaorui Guo, Maqbool Ahmad
2020 IEEE Access  
Antifractals are generated by applying a map recursively to an initial point in complex plane that have become a significant area of research these days.  ...  Complex graphics of nonlinear dynamical systems perform vital role in many fields, e.g., image compression or encryption, art, science, and so on.  ...  Recently, in [22] , [23] authors used Noor orbit and modified S-iteration orbit to generate tricorns and multicorns with s-convextity. Chugh et al.  ... 
doi:10.1109/access.2020.2983474 fatcat:uga6csrwj5gohb6ec77eig4v7u

Fixed point results for Fractal generation of complex polynomials involving Sine function via Non-standard iterations

Hengxiao Qi, Muhammad Tanveer, Waqas Nazeer, Yu-Ming Chu
2020 IEEE Access  
Nowadays researchers use different techniques to generate beautiful fractals for a complex polynomial z n + c.  ...  Noor, CR and SP iterations) have same escape radii for any complex polynomial, so we use these results for S, CR and SP iterations also to apply for the generation of Julia and Mandelbrot sets with sin  ...  versions of S, Noor, CR and SP iterations in [42] , [43] , [44] and [45] to generalize the fractals.  ... 
doi:10.1109/access.2020.3018090 fatcat:e3ftf7bk2fdivkswxdnkhaifv4

Some New Iterative Algorithms for Solving One-Dimensional Non-Linear Equations and Their Graphical Representation

Amir Naseem, M. A. Rehman, Thabet Abdeljawad
2021 IEEE Access  
the fractal behavior and dynamical aspects of the proposed iterative algorithms.  ...  Solving non-linear equation is perhaps one of the most difficult problems in all of numerical computations, especially in a diverse range of engineering applications.  ...  They presented graphical examples by means of Jungck-CR iteration process with s-convexity.  ... 
doi:10.1109/access.2021.3049428 fatcat:orojtxkf7zcgzd2qattj2lkyei

Lacunary Möbius Fractals on the Unit Disk

L. K. Mork, Keith Sullivan, Darin J. Ulness
2021 Symmetry  
The behavior, dimension, dynamics, and sensitivity of filled-in Julia sets and Mandelbrot sets to variables will be discussed in detail.  ...  In the recent engineering literature, Nazeer and Kang intensely studied Jungck Mann orbits and fractal generating along with escape time algorithms for finite polynomials based on the concept of S-convexity  ...  Fractal Dimension In this work, fractal dimension was calculated using a modified version of the Hausdorff dimension that was developed in reference [2] to which the reader is referred.  ... 
doi:10.3390/sym13010091 fatcat:eok446pklzhplj52ab3uautksq

Novel Iteration Schemes for Computing Zeros of Non-Linear Equations with Engineering Applications and Their Dynamics

Amir Naseem, M. A. Rehman, Thabet Abdeljawad, Yu-Ming Chu
2021 IEEE Access  
In 2016, the authors modified the Abbasbandy's method [1] and then presented polynomiographs through the modified method [20] .  ...  They presented graphical examples by means of Jungck-CR iteration process with s-convexity.  ...  the form of polynomiographs are presented in Fig. 3 .  ... 
doi:10.1109/access.2021.3091473 fatcat:mkv4ty7ywfcy3nj4n56sh2rcca