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

作　　者：Honey Sharma 

机构地区：[1]Dr.B.R.Ambedkar National Institute of Technology

出　　处：《Analysis in Theory and Applications》2011年第1期40-50,共11页分析理论与应用（英文刊）

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.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.

关 键 词：q- integers q-Bernstein polynomials A-statistical convergence modulus ofcontinuity Lipschitz class Peetre＇s type K-functional 

分 类 号：O174.14[理学—数学]