Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (1): 142-153.

• Articles • Previous Articles     Next Articles

The Errors of Simultaneous Approximation by Bernstein Type |Operators

DING Chun-Mei   

  1. College of Science, China Jiliang University, Hangzhou 310018
  • Received:2008-06-07 Revised:2009-08-06 Online:2010-01-01 Published:2010-01-01
  • Supported by:

    国家自然科学基金(90818020)和浙江省自然科学基金(Y7080235)资助.

Abstract:

In this paper,  we show that the functions in space C[0,1] and their derivatives can be simultaneously approximated by the combinations of the Bernstein operators. Both direct and inverse theorems are proved.   An equivalence relation between the derivatives of  the Bernstein operators and the smoothness of function is obtained as well.  These results bridge the gap between the classical  pointwise conclusions and the  global conclusions for simultaneous approximation by the Bernstein operators.

Key words: Bernstein operators, Simultaneous approximation, Direct theorem, Inverse theorem, Derivatives

CLC Number: 

  • 41A28
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