论文标题
同时近端集的总和
On the sum of simultaneously proximinal sets
论文作者
论文摘要
在本文中，我们表明，紧凑型凸子集的总和和同时$τ$ - 近端的近端凸出子集（同时分别近似$τ$ -Compact subset x）x x x x同时是tau tau近近近似$ y mimaltimally近似$ - 同时组合$ - 子集和同时近似弱紧凑的X子集的X的子集仍然近似弱紧凑，其中$τ$是标准或弱拓扑。此外，提出了有关同时近端子空间总和的一些相关结果。
In this paper, we show that the sum of a compact convex subset and a simultaneously $τ$-strongly proximinal convex subset (resp. simultaneously approximatively $τ$-compact convex subset) of a Banach space X is simultaneously tau-strongly proximinal (resp. simultaneously approximatively $τ$-compact ), and the sum of weakly compact convex subset and a simultaneously approximatively weakly compact convex subset of X is still simultaneously approximatively weakly compact, where $τ$ is the norm or the weak topology. Moreover, some related results on the sum of simultaneously proximinal subspaces are presented.
