The Rate of Convergence of Lupas q-Analogue of the Bernstein Operators

We discuss the rate of convergence of the Lupas q-analogues of the Bernstein operators Rn,q(f;x) which were given by Lupas in 1987. We obtain the estimates for the rate of convergence of Rn,q(f) by the modulus of continuity of f, and show that the estimates are sharp in the sense of order for Lipsch...

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Main Authors: Heping Wang, Yanbo Zhang
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/521709
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author Heping Wang
Yanbo Zhang
author_facet Heping Wang
Yanbo Zhang
author_sort Heping Wang
collection DOAJ
description We discuss the rate of convergence of the Lupas q-analogues of the Bernstein operators Rn,q(f;x) which were given by Lupas in 1987. We obtain the estimates for the rate of convergence of Rn,q(f) by the modulus of continuity of f, and show that the estimates are sharp in the sense of order for Lipschitz continuous functions.
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institution Kabale University
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publishDate 2014-01-01
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spelling doaj-art-371bd8548e2e43db9a24b3cddd63c5a42025-02-03T01:22:10ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/521709521709The Rate of Convergence of Lupas q-Analogue of the Bernstein OperatorsHeping Wang0Yanbo Zhang1School of Mathematical Sciences, BCMIIS, Capital Normal University, Beijing 100048, ChinaDepartment of Basic Courses, Shandong Modern Vocational College, Jinan, Shandong 250104, ChinaWe discuss the rate of convergence of the Lupas q-analogues of the Bernstein operators Rn,q(f;x) which were given by Lupas in 1987. We obtain the estimates for the rate of convergence of Rn,q(f) by the modulus of continuity of f, and show that the estimates are sharp in the sense of order for Lipschitz continuous functions.http://dx.doi.org/10.1155/2014/521709
spellingShingle Heping Wang
Yanbo Zhang
The Rate of Convergence of Lupas q-Analogue of the Bernstein Operators
Abstract and Applied Analysis
title The Rate of Convergence of Lupas q-Analogue of the Bernstein Operators
title_full The Rate of Convergence of Lupas q-Analogue of the Bernstein Operators
title_fullStr The Rate of Convergence of Lupas q-Analogue of the Bernstein Operators
title_full_unstemmed The Rate of Convergence of Lupas q-Analogue of the Bernstein Operators
title_short The Rate of Convergence of Lupas q-Analogue of the Bernstein Operators
title_sort rate of convergence of lupas q analogue of the bernstein operators
url http://dx.doi.org/10.1155/2014/521709
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