论文标题
最佳近端对的独特性和半标空间的刚性
Uniqueness of best proximity pairs and rigidity of semimetric spaces
论文作者
论文摘要
对于任意的半学空间$（x，d）$和近乎连接的近端子集$ a $ a $，$ b $ $ x $，我们将近端图定义为具有零件$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a和$ b $的近视$ \ \ \ {a，b \ b \ b \ b \ b \ b \ b \ b \ b \ b $满足等价$ d（a，b）= \ operatateRaneorneorn $ a的两部分图。我们表征其近端图最多具有一个边缘的半学空间，而近端图的半学空间的顶点最多只有$ 1 $。这使我们能够描述必要和充分的条件，以实现最佳近端对和最佳近似值的独特性。
For arbitrary semimetric space $(X, d)$ and disjoint proximinal subsets $A$, $B$ of $X$ we define the proximinal graph as a bipartite graph with parts $A$ and $B$ whose edges $\{a, b\}$ satisfy the equality $d(a, b) = \operatorname{dist}(A, B)$. We characterize the semimetric spaces whose proximinal graphs have at most one edge and the semimetric spaces whose proximinal graphs have the vertices with degree at most $1$ only. This allows us to describe the necessary and sufficient conditions for uniqueness of the best proximity pairs and best approximations.
