IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v479y2024ics009630032400362x.html
   My bibliography  Save this article

Analytical properties and the box-counting dimension of nonlinear hidden variable recurrent fractal interpolation functions constructed by using Rakotch's fixed point theorem

Author

Listed:
  • Ro, ChungIl
  • Yun, CholHui

Abstract

Rakotch contraction is a generalization of Banach contraction, which implies that in the case of using Rakotch's fixed point theorem, we can model more objects than using Banach's fixed point theorem. Moreover, hidden variable recurrent fractal interpolation functions (HVRFIFs) with Hölder function factors are more general than the fractal interpolation functions (FIFs), recurrent FIFs and hidden variable FIFs with Lipschitz function factors. We demonstrate that HVRFIFs can be constructed using the Rakotch's fixed point theorem, and then investigate the analytical and geometric properties of those HVRFIFs. Firstly, we construct a nonlinear hidden variable recurrent fractal interpolation functions with Hölder function factors on the basis of a given data set using Rakotch contractions. Next, we analyze the smoothness of the HVRFIFs and show that they are stable on the small perturbations of the given data. Finally, we get the lower and upper bounds for their box-counting dimensions.

Suggested Citation

  • Ro, ChungIl & Yun, CholHui, 2024. "Analytical properties and the box-counting dimension of nonlinear hidden variable recurrent fractal interpolation functions constructed by using Rakotch's fixed point theorem," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    • Handle: RePEc:eee:apmaco:v:479:y:2024:i:c:s009630032400362x
    DOI: 10.1016/j.amc.2024.128901
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630032400362X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2024.128901?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mi-Gyong Ri & Chol-Hui Yun, 2021. "Smoothness And Fractional Integral Of Hidden Variable Recurrent Fractal Interpolation Function With Function Vertical Scaling Factors," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(06), pages 1-17, September.
    2. Manuj Verma & Amit Priyadarshi, 2024. "Fractal Surfaces Involving Rakotch Contraction For Countable Data Sets," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-12.
    3. Yun, CholHui & Ri, MiGyong, 2020. "Box-counting dimension and analytic properties of hidden variable fractal interpolation functions with function contractivity factors," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Ri, Mi-Gyong & Yun, Chol-Hui, 2022. "Riemann-Liouville fractional derivatives of hidden variable recurrent fractal interpolation functions with function scaling factors and box dimension," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    5. JinMyong Kim & HyonJin Kim & HakMyong Mun, 2020. "Nonlinear fractal interpolation curves with function vertical scaling factors," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 483-499, June.
    Full references (including those not matched with items on IDEAS)

    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. Ri, Mi-Gyong & Yun, Chol-Hui, 2022. "Riemann-Liouville fractional derivatives of hidden variable recurrent fractal interpolation functions with function scaling factors and box dimension," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Ri, Mi-Gyong & Yun, Chol-Hui, 2020. "Riemann Liouville fractional integral of hidden variable fractal interpolation function," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Ri, SongIl, 2021. "A remarkable fact for the box dimensions of fractal interpolation curves of R3," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Yao, Kui & Chen, Haotian & Peng, W.L. & Wang, Zekun & Yao, Jia & Wu, Yipeng, 2021. "A new method on Box dimension of Weyl-Marchaud fractional derivative of Weierstrass function," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Agathiyan, A. & Gowrisankar, A. & Fataf, Nur Aisyah Abdul, 2024. "On the integral transform of fractal interpolation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 222(C), pages 209-224.

    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:eee:apmaco:v:479:y:2024:i:c:s009630032400362x. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.