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On (p, q)-analogue of Kantorovich type Bernstein–Stancu–Schurer operators

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  • Cai, Qing-Bo
  • Zhou, Guorong

Abstract

In this paper, we introduce a new kind of Kantorovich-type Bernstein–Stancu–Schurer operators based on the concept of (p, q)-integers. We investigate statistical approximation properties and establish a local approximation theorem, we also give a convergence theorem for the Lipschitz continuous functions. Finally, we give some graphics and numerical examples to illustrate the convergence properties of operators to some functions.

Suggested Citation

  • Cai, Qing-Bo & Zhou, Guorong, 2016. "On (p, q)-analogue of Kantorovich type Bernstein–Stancu–Schurer operators," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 12-20.
    • Handle: RePEc:eee:apmaco:v:276:y:2016:i:c:p:12-20
    DOI: 10.1016/j.amc.2015.12.006
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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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    Cited by:

    1. Mursaleen, M. & Naaz, Ambreen & Khan, Asif, 2019. "Improved approximation and error estimations by King type (p, q)-Szász-Mirakjan Kantorovich operators," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 175-185.
    2. Liang Zeng & Qing-Bo Cai & Xiao-Wei Xu, 2020. "A -Statistical Convergence Properties of Kantorovich Type λ -Bernstein Operators Via ( p , q )-Calculus," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
    3. Ravi P. Agarwal & Hana Al-Hutami & Bashir Ahmad, 2022. "On Solvability of Fractional ( p , q )-Difference Equations with ( p , q )-Difference Anti-Periodic Boundary Conditions," Mathematics, MDPI, vol. 10(23), pages 1-14, November.

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