Chinese Quarterly Journal of Mathematics ›› 2008, Vol. 23 ›› Issue (4): 559-564.

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On Double Revised Nodes of S N Bernstein Interpolation Process of the Third Type

  

  1. 1. Department of Mathematics,Baicheng Teacher's College,Baicheng 137000,China2. Department of Mathematics and Information Science,Yantai University,Yantai 264005,China
  • Received:2004-09-22 Online:2008-12-30 Published:2023-09-15
  • About author: CHANG Yu-bao(1970-), male, native of Baicheng, Jilin, a lecturer of Baicheng Teacher's College, M.S.D, engages in function approximation theory.
  • Supported by:
    Supported by the National Natural Science Foundation of China(10626045);

Abstract: In this work, the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step. An operator is constructed by revising double interpolation nodes. It is proved that the operator converges to arbitrary continuous functions uniformly and the convergence order is the best.

Key words:  interpolation polynomial, uniform convergence, the highest convergence order, S N Bernstein problem

CLC Number: