IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i18p3324-d914017.html
   My bibliography  Save this article

Dynamics of RK Iteration and Basic Family of Iterations for Polynomiography

Author

Listed:
  • Lateef Olakunle Jolaoso

    (Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Medunsa 0204, South Africa
    School of Mathematical Sciences, University of Southampton, Highfield SO17 3AS, UK)

  • Safeer Hussain Khan

    (Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54000, Pakistan)

  • Kazeem Olalekan Aremu

    (Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Medunsa 0204, South Africa
    Department of Mathematical Sciences, Usmanu Danfodiyo University, Sokoto 840004, Nigeria)

Abstract

In this paper, we propose some modifications of the basic family of iterations with a new four-step iteration called RK iteration and its s -convexity. We present some graphical examples showing the dynamics of the new iteration in the colouring and shapes of the obtained polynomiographs compared to the ones from the basic family only. Moreover, the computational results reveal that the value of s in the s -convex combination of the RK iteration has a significant impact on the time taken by the iteration process for approximating the roots of the polynomials. The obtained results are interesting from an artistic and computational point of view.

Suggested Citation

  • Lateef Olakunle Jolaoso & Safeer Hussain Khan & Kazeem Olalekan Aremu, 2022. "Dynamics of RK Iteration and Basic Family of Iterations for Polynomiography," Mathematics, MDPI, vol. 10(18), pages 1-16, September.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3324-:d:914017
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/18/3324/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/18/3324/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lateef Olakunle Jolaoso & Safeer Hussain Khan, 2020. "Some Escape Time Results for General Complex Polynomials and Biomorphs Generation by a New Iteration Process," Mathematics, MDPI, vol. 8(12), pages 1-18, December.
    2. T. Lotfi & F. Soleymani & S. Sharifi & S. Shateyi & F. Khaksar Haghani, 2014. "Multipoint Iterative Methods for Finding All the Simple Zeros in an Interval," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-13, July.
    3. Krzysztof Gdawiec & Wiesław Kotarski & Agnieszka Lisowska, 2015. "Polynomiography Based on the Nonstandard Newton-Like Root Finding Methods," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-19, February.
    4. Gdawiec, Krzysztof & Kotarski, Wiesław, 2017. "Polynomiography for the polynomial infinity norm via Kalantari’s formula and nonstandard iterations," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 17-30.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tanveer, Muhammad & Nazeer, Waqas & Gdawiec, Krzysztof, 2023. "On the Mandelbrot set of zp+logct via the Mann and Picard–Mann iterations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 184-204.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lateef Olakunle Jolaoso & Safeer Hussain Khan, 2020. "Some Escape Time Results for General Complex Polynomials and Biomorphs Generation by a New Iteration Process," Mathematics, MDPI, vol. 8(12), pages 1-18, December.
    2. Bisheh-Niasar, Morteza & Gdawiec, Krzysztof, 2019. "Bisheh-Niasar–Saadatmandi root finding method via the S-iteration with periodic parameters and its polynomiography," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 160(C), pages 1-12.
    3. Kumari, Sudesh & Gdawiec, Krzysztof & Nandal, Ashish & Postolache, Mihai & Chugh, Renu, 2022. "A novel approach to generate Mandelbrot sets, Julia sets and biomorphs via viscosity approximation method," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    4. Muhammad Tanveer & Waqas Nazeer & Krzysztof Gdawiec, 2020. "New Escape Criteria for Complex Fractals Generation in Jungck-CR Orbit," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1285-1303, December.
    5. Tanveer, Muhammad & Nazeer, Waqas & Gdawiec, Krzysztof, 2023. "On the Mandelbrot set of zp+logct via the Mann and Picard–Mann iterations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 184-204.
    6. Panadda Thongpaen & Rattanakorn Wattanataweekul, 2021. "A Fast Fixed-Point Algorithm for Convex Minimization Problems and Its Application in Image Restoration Problems," Mathematics, MDPI, vol. 9(20), pages 1-13, October.
    7. Deepak Kumar & Sunil Kumar & Janak Raj Sharma & Lorentz Jantschi, 2021. "Convergence Analysis and Dynamical Nature of an Efficient Iterative Method in Banach Spaces," Mathematics, MDPI, vol. 9(19), pages 1-16, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3324-:d:914017. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.