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The Kantorovich variant of an operator defined by D. D. Stancu

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  • Kajla, Arun

Abstract

In this note we introduce Kantorovich variant of the operators considered by Stancu (1998) based on two nonnegative parameters. Here, we prove an approximation theorem with the help of Bohman–Korovkin’s principle and find the estimate of the rate of convergence by means of modulus of smoothness and Lipschitz type function for these operators. In the last section of the paper, we show the convergence of the operators by illustrative graphics in Mathematica to certain functions.

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  • 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.
    • Handle: RePEc:eee:apmaco:v:316:y:2018:i:c:p:400-408
    DOI: 10.1016/j.amc.2017.08.021
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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. Kajla, Arun & Agrawal, P.N., 2015. "Szász–Durrmeyer type operators based on Charlier polynomials," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1001-1014.
    3. 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.
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