Best approximation by closed unit balls

Subject Areas : Applied Mathematics

H. R. Kamali ¹ (Department of Mathematics,Ardakan Branch,Islamic Azad university,Ardakan,Iran.)
H. Mazaheri ² (Faculty of Mathematics, Yazd University, Yazd, Iran.)
H. R. Khadezadeh ³ (Faculty of Mathematics, Yazd University, Yazd, Iran.)
H. Ardakani ⁴ (Faculty of Mathematics, Yazd University, Yazd, Iran.)

Received: 2015-09-13 Accepted : 2015-09-13 Published : 2014-05-01

Keywords:

Abstract :

We obtain a sucint and nesessery theoreoms simple for compactness andweakly compactness of the best approximate sets by closed unit balls. Also weconsider relations Kadec-Klee property and shur property with this objects.These theorems are extend of papers mohebi and Narayana.

References:

[1] F. Deutsch, Best approximation in inner product spaces., CMS Books in
Mathematics/Ouvrages de Mathmatiques de la SMC, 7. Springer-Verlag,
New York, 2001.
[2] H. Mohebi, On quasi-Chebyshev subspaces of Banach spaces. J. Approx.
Theory 107 (2000), no. 1, 87-95.
[3] H. Mohebi, On quasi-Chebyshev subspaces of Banach spaces. J. Approx.
Theory 107 (2000), no. 1, 87-95.
[4] Narayana, Darapaneni, T. S. S. R. K. Rao, Some remarks on quasi-
Chebyshev subspaces. J. Math. Anal. Appl. 321 (2006), no. 1, 193{197.
[5] I. Singer, The theory of best approximation and functional analysis.
Conference Board of the Mathematical Sciences Regional Conference
Series in Applied Mathematics, No. 13. 1974.
[6] I. Singer, Best approximation in normed linear spaces by elements of linear
subspaces. Springer-Verlag, New York-Berlin 1970.
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