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On a sequence of linear and positive operators. (English) Zbl 1199.41139
Summary: In order to approximate a function $$f:[0,\infty ]\to\mathbb R$$ where $$| f(x)|\leq Mx^{\alpha}$$ for $$x>0$$ and $$M=M(f)>0$$, we introduce the approximation operators $${\mathcal F}_n$$ given by: $({\mathcal F}_n f)(x)=\frac {{(nx)}_{n+1}}{n!} \int_0^1 t^{nx-1} {(1-t)}^n f\left(\frac t{1-t}\right)\,dt,\;x>0,\;\alpha >0,$ where $$n\geq n_0$$, $$n_0 =[\alpha ]+b+1$$ and $$n\in {\mathbb N}^*$$ is fixed.
Our aim is to find some properties for the above operator.
##### MSC:
 41A36 Approximation by positive operators
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