Sahai, Ashok; Prasad, Govind On simultaneous approximation by modified Lupas operators. (English) Zbl 0596.41035 J. Approximation Theory 45, 122-128 (1985). A ”modified Lupas operator” is defined, for functions integrable in \([0,+\infty)\), in the following way: \[ (M_ nf)(x)=(n- 1)\sum^{\infty}_{k=0}P_{n,k}(x)\int^{\infty}_{0}P_{n,k}(y)\quad f(y)dy, \] where \[ P_{n,k}(t)={n+k-1\choose k}t^ k/(1+t)^{n+k}. \] Two general theorems, concerning the approximation of functions with these operators, are given. If we set \(A_ r=M_ n^{(r)}f(x)-f^{(r)}(x),\) then we can say that the first theorem deals with \(\lim_{n\to \infty}| A_ r|\), when f has a derivative of \((r+2)th\) order; the second one gives an estimate of \(\| A_ r\|\) in terms of the modulus of continuity of \(f^{(r)}\). Reviewer: P.L.Papini Cited in 4 ReviewsCited in 42 Documents MSC: 41A36 Approximation by positive operators 41A25 Rate of convergence, degree of approximation Keywords:modified Lupas operator; modulus of continuity PDFBibTeX XMLCite \textit{A. Sahai} and \textit{G. Prasad}, J. Approx. Theory 45, 122--128 (1985; Zbl 0596.41035) Full Text: DOI References: [1] Derriennic, M. M., Sur l’approximation de fonctions integrables sur [0, 1] par des polynomes de Bernstein modifies, J. Approx. Theory, 31, 325-343 (1981) · Zbl 0475.41025 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.