[1] He Jinsu**, Li Chong,. Strong Uniqueness of Best Approximationsfrom RS-sets in Banach Spaces* [J]. Journal of Southeast University (English Edition), 2001, 17 (1): 70-72. [doi:10.3969/j.issn.1003-7985.2001.01.016]

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Strong Uniqueness of Best Approximationsfrom RS-sets in Banach Spaces^*()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

17

Issue:

2001 1

Page:

70-72

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2001-06-30

Info

Title:

Strong Uniqueness of Best Approximationsfrom RS-sets in Banach Spaces^*

Author(s):

He Jinsu^1**;  Li Chong²

¹College of Mathematics, Physics and Information Sciences, Zhejiang Normal University, Jinhua 321004, China
²Department of Applied Mathematics, Southeast University, Nanjing 210096, China

Keywords:

best approximation;  RS-set;  strong uniqueness

PACS:

O177.92

DOI:

10.3969/j.issn.1003-7985.2001.01.016

Abstract:

The problem of strong uniqueness of best approximation from an RS-set in a Banach space is considered. For a fixed RS-set G and an element x∈X, we proved that the best approximation g^* to x from G is strongly unique.

References:

[1] D.Braess, Nonlinear approximation theory, Springer-Verlag, New York, 1986
[2] I.Singer, Best approximation in normed linear spaces by elements of linear subspaces, Springer-Verlag, Berlin-Heidelberg-New York, 1970
[3] S.Y.Xu, C.Li, and W.S.Yang, Nonlinear approximation theory in Banach spaces(In Chinese), Science Press, Beijing, 1998
[4] E.R.Rozema, and P.W.Smith, Global approximation with bounded coefficients, J. Approx. Theory, vol.16, pp.162-174, 1976
[5] D.Amir, Uniqueness of best simultaneous approximations and strictly interpolating subspaces, J. Approx. Theory, vol.40, pp.196-201, 1984
[6] C.Li, Best simultaneous approximation by RS-sets, Numer. Math., JCU(In Chinese), vol.15, pp.62-71, 1993
[7] C.Li, A class of best simultaneous approximation problems, Computer Math. Applic., vol. 31, pp.45-53, 1996
[8] X.F.Luo, J.S.He, and C.Li, On best simultaneous approximation from suns to an infinite sequence in Banach spaces, Acta Math. Sinica, to be published, 2001

Memo

Memo:

* The project supported by the National Natural Science Foundation of China(19971013)and Jiangsu Provincial(BK99001)Natural Science Foundation.
** Born in 1965, female, lecturer.

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