(untitled) (European Journal of Pure and Applied Mathematics, 2023)
In this paper, we study strong coproximinality in Bochner L^p-spaces and in the Köthe Bochner function space E(X). We investigate some conditions to be imposed on the subspace G of the Banach space X such that L^p(μ,G ) is strongly coproximinal in L^p(μ,X ), 1 ≤ p <∞. On the other hand, we prove that if G is a separable subspace of X then G is strongly coproximinal in X if and only if E(G) is strongly coproximinal in E(X), provided that E is a strictly monotone Köthe space. This generalizes some results in the literature. Some other results in this direction are also presented.