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Approximation by Bivariate (p, q)-Bernstein–Kantorovich Operators

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Abstract

In the present paper, we introduce Kantorovich modifications of (p, q)-Bernstein operators for bivariate functions using a new (p, q)-integral. We first estimate the moments and central moments. We give the uniform convergence of new operators, rate of convergence in terms of modulus of continuity. The approximations behaviours of the operators for functions having continuous partial derivatives and for functions belong to Lipschitz class are investigated as well.

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Acknowledgments

The authors gratefully acknowledge the financial support from King Abdulaziz University, Jeddah, Saudi Arabia.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Arts, Kirikkale University, Yahsihan, 71450, Kirikkale, Turkey

    Tuncer Acar & Ali Aral

  2. Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    S. A. Mohiuddine

Authors
  1. Tuncer Acar
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  2. Ali Aral
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  3. S. A. Mohiuddine
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Correspondence to Tuncer Acar.

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Acar, T., Aral, A. & Mohiuddine, S.A. Approximation by Bivariate (p, q)-Bernstein–Kantorovich Operators. Iran J Sci Technol Trans Sci 42, 655–662 (2018). https://doi.org/10.1007/s40995-016-0045-4

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  • DOI: https://doi.org/10.1007/s40995-016-0045-4

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