IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v294y2017icp318-331.html
   My bibliography  Save this article

Approximation of Baskakov type Pólya–Durrmeyer operators

Author

Listed:
  • Gupta, Vijay
  • Acu, Ana Maria
  • Sofonea, Daniel Florin

Abstract

In the present paper we propose the Durrmeyer type modification of Baskakov operators based on inverse Pólya–Eggenberger distribution. First we estimate a recurrence relation by using hypergeometric series. We give a global approximation theorem in terms of second order modulus of continuity, a direct approximation theorem by means of the Ditzian–Totik modulus of smoothness and a Voronovskaja type theorem. Some approximation results in weighted space are obtained. Also, we show the rate of convergence of these operators to certain functions by illustrative graphics using the Maple algorithms.

Suggested Citation

  • Gupta, Vijay & Acu, Ana Maria & Sofonea, Daniel Florin, 2017. "Approximation of Baskakov type Pólya–Durrmeyer operators," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 318-331.
    • Handle: RePEc:eee:apmaco:v:294:y:2017:i:c:p:318-331
    DOI: 10.1016/j.amc.2016.09.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316305720
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.09.012?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Deo, Naokant & Dhamija, Minakshi & Miclăuş, Dan, 2016. "Stancu–Kantorovich operators based on inverse Pólya–Eggenberger distribution," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 281-289.
    2. Agrawal, P.N. & Ispir, Nurhayat & Kajla, Arun, 2015. "Approximation properties of Bezier-summation-integral type operators based on Polya–Bernstein functions," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 533-539.
    3. Acar, Tuncer, 2015. "Asymptotic Formulas for Generalized Szász–Mirakyan Operators," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 233-239.
    4. Dhamija, Minakshi & Deo, Naokant, 2016. "Jain–Durrmeyer operators associated with the inverse Pólya–Eggenberger distribution," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 15-22.
    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. Kajla, Arun, 2018. "The Kantorovich variant of an operator defined by D. D. Stancu," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 400-408.

    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. Dhruv Bhatnagar, 2022. "Quantitative Theorems for a Rich Class of Novel Miheşan-type Approximation Operators Incorporating the Boas-Buck Polynomials," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(4), pages 1017-1035, December.
    2. Kajla, Arun, 2018. "The Kantorovich variant of an operator defined by D. D. Stancu," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 400-408.
    3. Dhamija, Minakshi & Deo, Naokant, 2016. "Jain–Durrmeyer operators associated with the inverse Pólya–Eggenberger distribution," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 15-22.
    4. Syed Abdul Mohiuddine & Arun Kajla & Abdullah Alotaibi, 2022. "Bézier-Summation-Integral-Type Operators That Include Pólya–Eggenberger Distribution," Mathematics, MDPI, vol. 10(13), pages 1-14, June.
    5. Adem Kilicman & Mohammad Ayman Mursaleen & Ahmed Ahmed Hussin Ali Al-Abied, 2020. "Stancu Type Baskakov—Durrmeyer Operators and Approximation Properties," Mathematics, MDPI, vol. 8(7), pages 1-13, July.

    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:apmaco:v:294:y:2017:i:c:p:318-331. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.