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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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