IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v202y2026ip1s0960077925015541.html

Coincidence, averages and fractals

Author

Listed:
  • Navascués, M.A.

Abstract

Countless problems of the applied and the social sciences can be formalized in terms of an equation of type Sx=Tx, where S and T are two mappings or operators on a common domain. Mathematically x is called a coincidence. This paper is devoted to the study of this kind of elements, in the context of b-metric and quasi-normed spaces, for a pair of maps satisfying a very general contractive condition. In the first place, the concept of Lyapunov and asymptotic stability of fixed points is extended to coincidences. Then a constructive theorem of existence of coincidence is given, which generalizes a classical result of Goebel. The theory is applied to the construction of a new type of fractal sets and fractal functions. Afterwards a recurrent algorithm to approximate coincidences is proposed, proving its convergence and stability. The particular case where the underlying space is Euclidean is considered, giving an iterative method to compute the sought points. Since the stability is sometimes related to a Jacobian matrix, an averaged method to find eigenvalues and singular values of matrices and infinite dimensional linear operators is developed. The algorithm proposed is used to compute the maximum singular value of the Volterra integral operator.

Suggested Citation

  • Navascués, M.A., 2026. "Coincidence, averages and fractals," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925015541
    DOI: 10.1016/j.chaos.2025.117541
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925015541
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.117541?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Ariza-Ruiz, D. & Garcia-Falset, J., 2015. "Iterative approximation to a coincidence point of two mappings," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 762-776.
    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. Keten Çopur, Ayşegül & Hacıoğlu, Emirhan & Gürsoy, Faik, 2024. "New insights on a pair of quasi-contractive operators in Banach spaces: Results on Jungck type iteration algorithms and proposed open problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 476-497.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:chsofr:v:202:y:2026:i:p1:s0960077925015541. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.