Best Simultaneous Approximation in Lp(I,E) Original Research Article

Let G be a reflexive subspace of the Banach space E and let Lp(I,E) denote the space of all p-Bochner integrable functions on the interval I=[0,1] with values in E, 1⩽p≺∞. Given any norm N(ċ,ċ) on R2, N nondecreasing in each coordinate on the set R2+, we prove that Lp(I,G) is N-simultaneously proximinal in Lp(I,E). Other results are also obtained.