Let G be a reflexive subspace of the Banach space E and let L(I, E) denote the space of all p-Bochner integrable functions on the interval I=[0, 1] with values in E, 1 [ pO.. Given any norm N(· , · ) on R, N nondecreasing in each coordinate on the set R +, we prove that L (I, G) is N-simultaneously proximinal in L(I, E). Other results are also obtained. © 2002 Elsevier Science (USA)
