Mercer, A. McD. A Bernstein-type operator approximating continuous functions on the half- line. (English) Zbl 0709.41020 Bull. Calcutta Math. Soc. 81, No. 2, 133-137 (1989). 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 Cited in 4 Documents MSC: 41A36 Approximation by positive operators Keywords:positive linear operator; Bernstein polynomials; inequalities Citations:Zbl 0437.41021 PDFBibTeX XMLCite \textit{A. McD. Mercer}, Bull. Calcutta Math. Soc. 81, No. 2, 133--137 (1989; Zbl 0709.41020)