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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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