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Approximation of Baskakov type Pólya–Durrmeyer operators

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  • 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
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    References listed on IDEAS

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    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. Acar, Tuncer, 2015. "Asymptotic Formulas for Generalized Szász–Mirakyan Operators," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 233-239.
    3. 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.
    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.
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    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.

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