Best Simultaneous Approximation in Orlicz Spaces

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.