IDEAS home Printed from https://ideas.repec.org/h/spr/spochp/978-1-4614-3498-6_14.html
   My bibliography  Save this book chapter

Fixed Point Approach to the Stability of the Quadratic Functional Equation

In: Nonlinear Analysis

Author

Listed:
  • Elqorachi Elhoucien

    (University Ibn Zohr)

  • Manar Youssef

    (University Ibn Zohr)

Abstract

In the present paper, we apply a fixed point theorem to prove the Hyers–Ulam–Rassias stability of the quadratic functional equation $$f(kx+ y)+f\bigl(kx+\sigma(y)\bigr)=2k^{2}f(x)+2f(y),\quad x,y\in E_{1} $$ from a normed space E 1 into a complete β-normed space E 2, where σ:E 1⟶E 1 is an involution and k is a fixed positive integer larger than 2. Furthermore, we investigate the Hyers–Ulam–Rassias stability for the functional equation in question on restricted domains. The concept of Hyers–Ulam–Rassias stability originated essentially with the Th.M. Rassias’ stability theorem that appeared in his paper “On the stability of linear mapping in Banach spaces” (Proc. Am. Math. Soc. 72:297–300, 1978).

Suggested Citation

  • Elqorachi Elhoucien & Manar Youssef, 2012. "Fixed Point Approach to the Stability of the Quadratic Functional Equation," Springer Optimization and Its Applications, in: Panos M. Pardalos & Pando G. Georgiev & Hari M. Srivastava (ed.), Nonlinear Analysis, edition 127, chapter 0, pages 259-277, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-3498-6_14
    DOI: 10.1007/978-1-4614-3498-6_14
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    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:spr:spochp:978-1-4614-3498-6_14. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.