BEST COAPPROXIMATION IN L∞(µ, X)

Let X be a real Banach space and let G be a closed subset of X. The set G is called coproximinal in X if for each x ∈ X, there exists y0 ∈ G such that ky − y0k ≤ kx − yk , for all y ∈ G. In this paper, we study coproximinality of L ∞(µ, G) in L ∞(µ, X), when G is either separable or reflexive coproximinal subspace of X.