journal6 ›› 2006, Vol. 27 ›› Issue (1): 9-16.

• Mathematics • Previous Articles     Next Articles

Characterizations of Best Simultaneous Approximation from Sets of Generalized Polynomials with Restricted Coefficients

  

  1. (College of Mathematics and Computer Science,Jishou University,Jishou 416000,Hunan China)
  • Online:2006-01-25 Published:2012-09-16
  • About author:LUO Xian-fa(1963-),male,was born in Jishou City,Hunan Province,associate professor of College of Mathematics and Computer Science,Jishou University,doctor;research area is nonlinear approximation theory in Banach spaces.
  • Supported by:

    The National Natural Science Foundation of China (10271025)

Abstract: This paper investigates the problem of the best weighted simultaneous approximation to totally bounded sequences (xv) from a set G of generalized polynomials with restricted coefficients in complex normed linear spaces X.By approximating a totally bounded sequence (xv) via sequences consisting of finite many points in X,and then by transforming the problem of the best simultaneous approximation to a sequence consisting of finite many points in X into that of the best Chebyshev approximation in a complex-valued continuous functions space,the author gives characteristic results of the best simultaneous approximation to (xv) from  G under the assumptions that X is uniformly smooth and infv∈Nd(xv,G)>0.

Key words: best simultaneous approximation, totally bounded sequence, characterization, monotonic norm, uniform smoothness

WeChat e-book chaoxing Mobile QQ