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Error estimates and the Voronovskaja theorem for modified Szász-Mirakyan operators. (English) Zbl 1108.41015
There is studied the following modification of the Szász-Mirakyan operators \[ A_n(f;r,q;x):= e^{-(n^q x+1)^r} \sum _{k=0}^{\infty } \frac {(n^q x+1)^{rk}} {k}!\, f\biggl (\frac {k}{n^q(n^q x+1)^{r-1}}\biggr ), \] where \(x\in [0,+\infty )\), \(n \in \mathbb N\), \(r \in [2,+\infty )\), and \(q>0\). There are given some estimates of the rate of convergence of \(A_n\) and proved the Voronovskaja type theorem involving \(A_n\).

MSC:
41A36 Approximation by positive operators
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References:
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