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GBS operators of Bernstein–Schurer–Kantorovich type based on q-integers

Author

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  • Sidharth, Manjari
  • Ispir, Nurhayat
  • Agrawal, P.N.

Abstract

Agrawal et al. (2015) constructed a bivariate generalization of a new kind of Kantorovich-type q-Bernstein–Schurer operators and studied a Voronovskaja type theorem and the rate of convergence in terms of the Lipschitz class function and the complete modulus of continuity. The concern of this paper is to obtain the degree of approximation for these bivariate operators in terms of the partial moduli of continuity and the Peetre’s K-functional. Finally, we construct the GBS (Generalized Boolean Sum) operators of bivariate q-Bernstein–Schurer–Kantorovich type and estimate the rate of convergence for these operators with the help of mixed modulus of smoothness.

Suggested Citation

  • Sidharth, Manjari & Ispir, Nurhayat & Agrawal, P.N., 2015. "GBS operators of Bernstein–Schurer–Kantorovich type based on q-integers," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 558-568.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:558-568
    DOI: 10.1016/j.amc.2015.07.052
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    References listed on IDEAS

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    1. Bărbosu, Dan & Muraru, Carmen Violeta, 2015. "Approximating B-continuous functions using GBS operators of Bernstein–Schurer–Stancu type based on q-integers," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 80-87.
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    Cited by:

    1. Baxhaku, Behar & Agrawal, Purshottam Narain, 2017. "Degree of approximation for bivariate extension of Chlodowsky-type q-Bernstein–Stancu–Kantorovich operators," Applied Mathematics and Computation, Elsevier, vol. 306(C), pages 56-72.

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