Fixed points of uniformly Lipschitzian mappings in spaces with uniformly normal structure
Fixed points of uniformly Lipschitzian mappings in spaces with uniformly normal structure
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DOI：
10.1016/0362-546x(85)90055-0
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发表时间：
1985
影响因子：
1.4
通讯作者：
E. Casini;E. Maluta
中科院分区：
文献类型：
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作者：
E. Casini;E. Maluta
设K是Banach空间X的闭凸有界子集。假设T：X！X是一致Lipschitz映射，即kTnx−Tnyk kx-yk对于所有x，y 2 K且n = 1，2，· · ·。证明了具有一致正规结构空间的一个不动点结果。这些是N（X）= sup{r（C，coC）：diamC = 1} < 1的空间，其中r（C，coC）表示集合C关于其凸闭包的切比雪夫半径。
Let K be a closed convex and bounded subset of a Banach space X. Suppose T:X ! X is a uniformly Lipschitzian mapping, i.e. kTnx−Tnyk kx−yk for all x, y 2 K and n = 1, 2, · · ·. We prove a fixed point result for a space having uniform normal structure. These are spaces for which N(X) = sup{r(C, coC): diamC = 1} < 1, where r(C, coC) denotes the Chebyshev radius of the set C with respect to its convex closure.