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Some approximation properties of bivariate Bleimann–Butzer–Hahn operators based on (p, q)-integers

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Abstract

In this paper, we apply (p, q)-calculus to construct generalized bivariate Bleimann–Butzer–Hahn operators based on (p, q)-integers and obtain Korovkin type approximation theorem. Furthermore, we compute the rate of convergence for these operators by using the modulus of continuity and Lipschitz type maximal function.

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Acknowledgments

Md. Nasiruzzaman acknowledges the financial support of BSR Fellowship of the University Grants Commission, New Delhi.

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Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    M. Mursaleen & Md. Nasiruzzaman

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

    M. Mursaleen

Authors
  1. M. Mursaleen
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  2. Md. Nasiruzzaman
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Correspondence to M. Mursaleen.

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Mursaleen, M., Nasiruzzaman, M. Some approximation properties of bivariate Bleimann–Butzer–Hahn operators based on (p, q)-integers. Boll Unione Mat Ital 10, 271–289 (2017). https://doi.org/10.1007/s40574-016-0080-2

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