International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 68017, 7 pages
doi:10.1155/2007/68017
Research Article
Best Simultaneous Approximation in Orlicz Spaces
1Mathematics Department, Hashimia University, P.O. Box 150459, Zarqa 13115, Jordan
2Mathematics Department, Yarmouk University, Irbed 21163, Jordan
Received 18 July 2006; Revised 14 January 2007; Accepted 17 April 2007
Academic Editor: Ricardo Estrada
Copyright © 2007 M. Khandaqji and Sh. Al-Sharif. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let X be a Banach space and let LΦ(I,X) denote the space of Orlicz X-valued integrable functions on the unit interval I equipped with the Luxemburg norm. In this paper, we present a distance formula dist(f1,f2,LΦ(I,G))Φ, where G is a closed subspace of X, and f1,f2∈LΦ(I,X). Moreover, some related results concerning best simultaneous approximation in LΦ(I,X) are presented.