APPROXIMATION PROPERTIES OF rth ORDER GENERALIZED BERNSTEIN POLYNOMIALS BASED ON q-CALCULUS

作     者：Honey Sharma 

作者机构：Dr.B.R.Ambedkar National Institute of Technology 

出 版 物：《Analysis in Theory and Applications》 (分析理论与应用（英文刊）)

年 卷 期：2011年第27卷第1期

页      面：40-50页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：q- integers q-Bernstein polynomials A-statistical convergence modulus ofcontinuity Lipschitz class Peetre's type K-functional 

摘      要：In this paper we introduce a generalization of Bernstein polynomials based on q calculus. With the help of Bohman-Korovkin type theorem, we obtain A-statistical approximation properties of these operators. Also, by using the Modulus of continuity and Lipschitz class, the statistical rate of convergence is established. We also gives the rate of A-statistical convergence by means of Peetre＇s type K-functional. At last, approximation properties of a rth order generalization of these operators is discussed.