IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-31317-7_14.html
   My bibliography  Save this book chapter

A Survey on Durrmeyer-Type Operators

In: Contributions in Mathematics and Engineering

Author

Listed:
  • Vijay Gupta

    (Netaji Subhas Institute of Technology, Department of Mathematics)

  • Themistocles M. Rassias

    (National Technical University of Athens, Department of Mathematics)

  • Jyoti Sinha

    (Inderprastha Engineering College, Department of Applied Mathematics)

Abstract

It is well known that discretely defined operators such as Bernstein polynomials, Baskakov operators, Szász–Mirakyan, Meyer-König–Zeller operators, Stancu operators, Jain operators, and their modified versions are not possible to approximate Lebesgue integrable functions. In the year 1930, Kantorovich proposed integral modification of the Bernstein polynomials. The more general integral modification of the Bernstein polynomial was given by Durrmeyer in the year 1967. After this several Durrmeyer-type modifications of different operators have been introduced and their approximation properties have been discussed. In the present note, to the best of our knowledge, we present the different Durrmeyer-type operators introduced in the last five decades. We also propose some open problems in the end.

Suggested Citation

  • Vijay Gupta & Themistocles M. Rassias & Jyoti Sinha, 2016. "A Survey on Durrmeyer-Type Operators," Springer Books, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Contributions in Mathematics and Engineering, pages 299-312, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-31317-7_14
    DOI: 10.1007/978-3-319-31317-7_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
    for a similarly titled item that would be available.

    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:spr:sprchp:978-3-319-31317-7_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.