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A -Statistical Convergence Properties of Kantorovich Type λ -Bernstein Operators Via ( p , q )-Calculus

Author

Listed:
  • Liang Zeng

    (School of Mathematical Sciences, Xiamen University, Xiamen 361005, China)

  • Qing-Bo Cai

    (School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China)

  • Xiao-Wei Xu

    (School of Computer and Data Engineering, Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China)

Abstract

In the present paper, Kantorovich type λ -Bernstein operators via ( p , q )-calculus are constructed, and the first and second moments and central moments of these operators are estimated in order to achieve our main results. An A -statistical convergence theorem and the rate of A -statistical convergence theorems are obtained according to some analysis methods and the definitions of A -statistical convergence, the rate of A -statistical convergence and modulus of smoothness.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:291-:d:323296
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    References listed on IDEAS

    as
    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. 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. 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.
    5. 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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