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Korovkin-type approximation properties of bivariate q-Meyer-König and Zeller operators

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Abstract

In the present paper, a bivariate generalization of the Meyer-König and Zeller operators based on the q-integers is constructed. Approximation properties and rate of convergence of these operators are established with the help of a Korovkin theorem for bivariate functions and a Korovkin-type theorem given by Heping [8] and Volkov [14] respectively.

Keywords: Positive linear operators, bivariate Korovkin theorem, bivariate modulus of continuity, bivariate Lipschitz class, q-integers.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Ankara University, Ankara, Turkey

    Ogün Doğru

  2. Department of Mathematics and Statistics, Auburn University, Auburn, AL, USA

    Vijay Gupta

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  1. Ogün Doğru
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  2. Vijay Gupta
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Doğru, O., Gupta, V. Korovkin-type approximation properties of bivariate q-Meyer-König and Zeller operators. Calcolo 43, 51–63 (2006). https://doi.org/10.1007/s10092-006-0114-8

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  • DOI: https://doi.org/10.1007/s10092-006-0114-8

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