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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 521709, 6 pages
http://dx.doi.org/10.1155/2014/521709
Research Article

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

1School of Mathematical Sciences, BCMIIS, Capital Normal University, Beijing 100048, China
2Department of Basic Courses, Shandong Modern Vocational College, Jinan, Shandong 250104, China

Received 24 December 2013; Accepted 12 January 2014; Published 9 April 2014

Academic Editor: Sofiya Ostrovska

Copyright © 2014 Heping Wang and Yanbo Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We discuss the rate of convergence of the Lupas -analogues of the Bernstein operators which were given by Lupas in 1987. We obtain the estimates for the rate of convergence of by the modulus of continuity of , and show that the estimates are sharp in the sense of order for Lipschitz continuous functions.