中文摘要：

设C是Banach空间X的弱紧凸集,D是X的可逼近凸集（相应地, 逼近弱紧凸集）.利用弱紧凸集中序列的收敛性, 证明了C＋D也是可逼近集（相应地,逼近弱紧集）,这是自反子空间与可逼近子空间的和（满足其和是闭的）仍然是可逼近子空间这一经典结论的推广和局部化.

英文摘要：

Let C be a weakly comapct convex subset of a Banach space X and D be a proximinal convex subset （respectively,approximatively weakly compact convex subset） of X.By using the convergence of the sequences in weakly compact convex sets,it is proved that C＋D is also a proximinal set（respectively,approximatively weakly compact set）.This generalizes the classical result that the sum of reflexive subspace and proximinal subspace（satisfying the sum is closed） is again proximinal.