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Some approximation results by (p, q)-analogue of Bernstein–Stancu operators

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  • Mursaleen, M.
  • Ansari, Khursheed J.
  • Khan, Asif

Abstract

In this paper, we introduce a new analogue of Bernstein–Stancu operators based on (p, q)-integers which we call as (p, q)-Bernstein–Stancu operators. We study approximation properties for these operators based on Korovkin’s type approximation theorem and also study some direct theorems. Furthermore, we give comparisons and some illustrative graphics for the convergence of operators to some function.

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  • 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.
    • Handle: RePEc:eee:apmaco:v:264:y:2015:i:c:p:392-402
    DOI: 10.1016/j.amc.2015.03.135
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    References listed on IDEAS

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    1. Mursaleen, M. & Khan, Faisal & Khan, Asif, 2014. "Statistical approximation for new positive linear operators of Lagrange type," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 548-558.
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    Cited by:

    1. Julalak Prabseang & Kamsing Nonlaopon & Jessada Tariboon & Sotiris K. Ntouyas, 2021. "Refinements of Hermite–Hadamard Inequalities for Continuous Convex Functions via ( p , q )-Calculus," Mathematics, MDPI, vol. 9(4), pages 1-12, February.
    2. 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.
    3. Mursaleen, M. & Ansari, Khursheed J. & Khan, Asif, 2016. "Erratum to ``On (p, q)-analogue of Bernstein Operators'' [Appl. Math. Comput. 266 (2015) 874–882]," Applied Mathematics and Computation, Elsevier, vol. 278(C), pages 70-71.
    4. 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.
    5. 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.
    6. Mursaleen, M. & Ansari, Khursheed J. & Khan, Asif, 2015. "Corrigendum to: “Some approximation results by (p, q)-analogue of Bernstein–Stancu operators” [Appl. Math. Comput. 264(2015)392–402]," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 744-746.

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