Voronovskaya type asymptotic approximation by modified gamma operators
type: Item
instance of: scholarly article
title: Voronovskaya type asymptotic approximation by modified gamma operators
zbMATH Open document ID: 1222.45009
author: Aydın İzgi
published in: Applied Mathematics and Computation
publication date: 2011-06-28T00:00:00Z
review text: \textit{A. Lupas} and \textit{M. Müller} [Math. Z. 98, 208--226 (1967; Zbl 0171.02301)] defined the gamma operators \(G_n(f;x)\). Recently \textit{A. İzgi} and \textit{I. Büyükyazici} [``Approximation in boundless interval and order of approximation'', Kastamonu E\"g itim dergisi II (2), 451--456 (2003)] modified the gamma operator as \(A_n(f;x)=\int_0^\infty K_n(x,t)f(t)\,dt\), defined for any \(f\) for which the last integral is convergent, where \(n=1,2,3,\dots\). The author establishes a Voronovskaya type asymptotic formula and obtains an error estimate formula for this modified gamma operator.
reviewed by: Kun Soo Chang
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 45M05
zbMATH DE Number: 5914119
zbMATH Keywords: gamma type operators
zbMATH Keywords: Voronovskaya formula
zbMATH Keywords: approximation
zbMATH Keywords: Taylor formula
zbMATH Keywords: error estimate formula
MaRDI profile type: Publication
full work available at URL: j.amc.2011.03.005
OpenAlex ID: W2035917434
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DOI: 10.1016/J.AMC.2011.03.005
description: scientific article; zbMATH DE number 5914119