IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n848540.html

Stability of the Exponential Functional Equation in Riesz Algebras

Author

Listed:
  • Bogdan Batko

Abstract

We deal with the stability of the exponential Cauchy functional equation F(x + y) = F(x)F(y) in the class of functions F : G → L mapping a group (G, +) into a Riesz algebra L. The main aim of this paper is to prove that the exponential Cauchy functional equation is stable in the sense of Hyers‐Ulam and is not superstable in the sense of Baker. To prove the stability we use the Yosida Spectral Representation Theorem.

Suggested Citation

  • Bogdan Batko, 2014. "Stability of the Exponential Functional Equation in Riesz Algebras," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:848540
    DOI: 10.1155/2014/848540
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/848540
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/848540?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
    ---><---

    References listed on IDEAS

    as
    1. Faruk Polat, 2012. "Some Generalizations of Ulam‐Hyers Stability Functional Equations to Riesz Algebras," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Faruk Polat, 2012. "Some Generalizations of Ulam-Hyers Stability Functional Equations to Riesz Algebras," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, January.
    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. Bogdan Batko, 2014. "On Approximate Solutions of Functional Equations in Vector Lattices," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

    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. Faruk Polat, 2012. "Approximate Riesz Algebra‐Valued Derivations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

    More about this item

    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:wly:jnlaaa:v:2014:y:2014:i:1:n:848540. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.