International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 245-252
Best approximation in Orlicz spaces
Department of Mathematics, Kuwait University, P.O. BOX 5969, Safat 130, Kuwait
Received 17 April 1989; Revised 23 December 1989
Copyright © 1991 H. Al-Minawi and S. Ayesh. 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.
Let be a real Banach space and be a finite measure space and be a
strictly icreasing convex continuous function on with . The space
is the set of all measurable functions with values in such that for some . One of the main results of this paper is:
For a closed subspace of , is proximinal in if and only if
is proximinal in . As a result if is reflexive subspace of ,
is proximinal in . Other results on proximinality of subspaces
of are proved.