Strong converse inequality for Szász-Durrmeyer operators
type: Item
instance of: scholarly article
title: Strong converse inequality for Szász-Durrmeyer operators
zbMATH Open document ID: 0876.41010
DOI: 10.1007/BF02664804
author: Song Li
published in: Applied Mathematics. Series B (English Edition)
publication date: 1997-11-20T00:00:00Z
review text: For the Szász-Durrmeyer operators \[ L_n(f,x)= n\sum^\infty_{k=0} s_{n,k}(x) \int^\infty_0 s_{n,k}(t)f(t)dt,\quad s_{n,k}(x)= e^{-nx}{(nx)^k\over k!} \] it is proved that for some \(m\), \[ \omega^2_\varphi(f,n^{-1/2})_p\leq M\{|L_n(f,x)- f|_p+ |L_{mn}(f,x)- f|_p\}, \] where \(\varphi(x)^2= x\), \(M>0\) and \(\omega^2_\varphi(f, t)_p\) denotes the second-order Ditzian-Totik modulus of smoothness.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A40
Mathematics Subject Classification ID: 41A27
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 947006
zbMATH Keywords: inverse inequality
zbMATH Keywords: Szasz-Durrmeyer operators
zbMATH Keywords: Ditzian-Totik modulus of smoothness
reviewed by: Margareta Heilmann
MaRDI profile type: Publication
cites work: Q3817079
cites work: Q3822651
cites work: Strong converse inequalities
full work available at URL: https://doi.org/10.1007/bf02664804
OpenAlex ID: W35646896
description: scientific article; zbMATH DE number 947006