International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 68017, 7 pages
doi:10.1155/2007/68017

Best simultaneous approximation in Orlicz spaces

M. Khandaqji1 and Sh. Al-Sharif2

1Mathematics Department, Hashimia University, P.O. Box 150459, Zarqa 13115, Jordan
 2Mathematics Department, Yarmouk University, Irbed 21163, Jordan

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.