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Some approximation results for Stancu type Lupaş–Schurer operators based on (p, q)-integers

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  • Kanat, K.
  • Sofyalıoğlu, M.

Abstract

In the present paper, we introduce the Stancu type generalisation of Lupaş–Schurer operators based on (p, q)-integers. We are concerned with the basic convergence of the constructed operators based on Korovkin’s type approximation theorem. Further, we obtain the rate of convergence for the new operators in terms of the modulus of continuity, with the help of functions of Lipschitz class and Peetre’s K-functionals. Then, we present three significant numerical mathematical algorithms. Finally, in order to confirm our theoretical results we obtain error estimation and illustrate the convergence of the (p, q)-Lupaş–Schurer–Stancu operators to certain functions by using MATLAB.

Suggested Citation

  • Kanat, K. & Sofyalıoğlu, M., 2018. "Some approximation results for Stancu type Lupaş–Schurer operators based on (p, q)-integers," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 129-142.
    • Handle: RePEc:eee:apmaco:v:317:y:2018:i:c:p:129-142
    DOI: 10.1016/j.amc.2017.08.046
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    References listed on IDEAS

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    1. Mursaleen, M. & Ansari, Khursheed J. & Khan, Asif, 2015. "On (p, q)-analogue of Bernstein operators," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 874-882.
    2. Mursaleen, M. & Ansari, Khursheed J. & Khan, Asif, 2015. "Some approximation results by (p, q)-analogue of Bernstein–Stancu operators," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 392-402.
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