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On (p, q)-analogue of Bernstein operators

Author

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

Abstract

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

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:874-882
    DOI: 10.1016/j.amc.2015.04.090
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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. 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.
    6. 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.
    7. Hari M. Srivastava & Khursheed J. Ansari & Faruk Özger & Zeynep Ödemiş Özger, 2021. "A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices," Mathematics, MDPI, vol. 9(16), pages 1-15, August.

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