Some Problems on Best Approximation in Orlicz Spaces

Garidi Wu, Dongyue Guan

College of Mathematics Science, Inner Mongolia Normal University, Huhhot, China.
College of Natural Science, Inner Mongolia Agricultural University, Huhhot, China.

DOI: 10.4236/am.2012.34048                

Abstract

In this paper we studied some problems on best approximation in Orlicz spaces, for which the approximating sets are Haar subspaces, the result of this paper can be considered as the extension of the classical corresponding result.

Keywords

Chebyshev System; Haar Subspace; Orlicz Space; Best Approximation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Y. S. Sun, “Approximation Theory of Functions,” Beijing Normal University Press, Beijing, 1989.
[2]	C. X. Wu and T. F. Wang, “Orlicz Space and Its Applications,” Hei Long Jiang Science and Technology Press, Harbin, 1983.
[3]	D. L. Xie, “The Characteristics of Best Approximators in Orlicz Spaces,” Journal of Hangzhou University, Vol. 12, No. 3, 1985, pp. 319-322.
[4]	Y. W. Wang and S. T. Chen, “The Best Approximating Operators in Orlicz Spaces,” Pure Mathematics and Applied Mathematics, Vol. 2, No. 2, 1986, pp. 44-51.
[5]	C. X. Wu, T. F. Wang, S. T. Chen and Y. W. Wang, “The Geometric Theory of Orlicz Spaces,” Harbin Industrial University Press, Harbin, 1986.
[6]	J. Gillis and G. Lewis, “Monic Polynomials with Minimal Norm,” Journal of Approximation Theory, Vol. 34, No. 2, 1982, pp. 187-193. doi:10.1016/0021-9045(82)90091-0