IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2012y2012i1n680456.html

Nθ‐Ward Continuity

Author

Listed:
  • Huseyin Cakalli

Abstract

A function f is continuous if and only if f preserves convergent sequences; that is, (f(αn)) is a convergent sequence whenever (αn) is convergent. The concept of Nθ‐ward continuity is defined in the sense that a function f is Nθ‐ward continuous if it preserves Nθ‐quasi‐Cauchy sequences; that is, (f(αn)) is an Nθ‐quasi‐Cauchy sequence whenever (αn) is Nθ‐quasi‐Cauchy. A sequence (αk) of points in R, the set of real numbers, is Nθ‐quasi‐Cauchy if lim r→∞(1/hr)∑k∈Ir|Δαk|=0, where Δαk = αk+1 − αk, Ir = (kr−1, kr], and θ = (kr) is a lacunary sequence, that is, an increasing sequence of positive integers such that k0 = 0 and hr : kr − kr−1 → ∞. A new type compactness, namely, Nθ‐ward compactness, is also, defined and some new results related to this kind of compactness are obtained.

Suggested Citation

  • Huseyin Cakalli, 2012. "Nθ‐Ward Continuity," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:680456
    DOI: 10.1155/2012/680456
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2012/680456
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/680456?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. İbrahim Çanak & Mehmet Dik, 2010. "New Types of Continuities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    2. Agata Caserta & Giuseppe Di Maio & Ljubiša D. R. Kočinac, 2011. "Statistical Convergence in Function Spaces," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-11, December.
    3. Agata Caserta & Giuseppe Di Maio & Ljubiša D. R. Kočinac, 2011. "Statistical Convergence in Function Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    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. Dimitrios Georgiou & Georgios Prinos, 2024. "A New Notion of Fuzzy Function Ideal Convergence," Mathematics, MDPI, vol. 12(2), pages 1-13, January.
    2. Bipan Hazarika, 2014. "Second Order Ideal-Ward Continuity," International Journal of Analysis, Hindawi, vol. 2014, pages 1-4, March.

    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:2012:y:2012:i:1:n:680456. 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.