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On strong approximation by modified Meyer-König and Zeller operators. (English) Zbl 1119.41022

The authors introduce certain Meyer-König and Zeller operators \(M_{n;r}\) in the space \(C^r_I\) of \(r\)th times differentiable functions \(f\) on a bounded interval \(I\). Also, they study strong differences \(H^q_{n;r}(f)\) for these operators. It is shown that the order of strong approximation of \(f\) in \(C^r_I\) by \(M_{n;r}(f)\) is better than that for classical Meyer-König and Zeller operators. This research was motivated by some questions raised in the book by L. Leindler [Budapest: Akadémiai Kiadó (1985; Zbl 0588.42001)].

MSC:

41A36 Approximation by positive operators

Citations:

Zbl 0588.42001
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