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A Bernstein-type operator approximating continuous functions on the half- line. (English) Zbl 0709.41020

G. Bleiman, P. L. Butzer and L. Hahn [Indagationes Math. 42, 255-262 (1980; Zbl 0437.41021)] introduced and studied the positive linear operator \(L_ n\) defined by \[ (L_ nf)(x)=(1+x)^{- n}\sum^{n}_{k=0}(n/k)f(k/(n-k-1))x^ k. \] The purpose of the present paper is to use the Bernstein polynomials as a starting point of the study of \(L_ n\). By this means, an analogue of Voronowskaya’s theorem for the Bernstein polynomials and sharper inequalities are obtained.
Reviewer: H.R.Dowson

MSC:

41A36 Approximation by positive operators

Citations:

Zbl 0437.41021
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