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Equivalent theorems on simultaneous approximation by combinations of Bernstein operatores

Authors:	Li Cheng Linsen Xie

Institution:	(1) Zhejiang Normal University, Jinhua, 321004, Zhejiang Province, P. R. China;(2) College of Mathematics and Physics, Lishui University, Lishui, 323000, Zhejiang Province, P. R. China

Abstract:	In this paper we give equivalent theorems on simultaneous approximation for the combinations of Bernstein operators by r-th Ditzian-Totik modulus of smoothness $\omega _{\varphi ^\lambda }^r (f,t)(0 \leqslant \lambda \leqslant 1)$ . We also investigate the relation between the derivatives of the combinations of Bernstein operators and the smoothness of derivatives of functions. Supported by the Key Academic Discipline of Zhejiang Provincial of China under Grant No.2005.

Keywords:	Bernstein operators combination simultaneous approximation moduli of smoothness BERNSTEIN SIMULTANEOUS APPROXIMATION THEOREMS relation modulus of smoothness derivatives functions paper equivalent theorems simultaneous approximation Bernstein operators
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