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Approximation theorems for generalized complex Kantorovich-type operators. (English) Zbl 1252.30023

Summary: The order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex \(q\)-Kantorovich polynomials \((q > 0)\) attached to analytic functions on compact disks are obtained. In particular, it is proved that for functions analytic in \(\{z \in \mathbb C : |z| < R\}\), \(R > q\), the rate of approximation by the \(q\)-Kantorovich operators \((q > 1)\) is of order \(q^{-n}\) versus \(1/n\) for the classical Kantorovich operators.

MSC:

30E10 Approximation in the complex plane
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