Fixed points of nonexpanding maps
Fixed points of nonexpanding maps
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DOI：
10.1090/s0002-9904-1967-11864-0
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发表时间：
1967-11
影响因子：
1.3
通讯作者：
B. Halpern
中科院分区：
文献类型：
--
作者：
B. Halpern
介绍。本文研究了实Hubert空间的单位球到自身的非展开映射。Browder[1]已经确定这样的地图总是至少有一个不动点。我们将发展一种类似于简单迭代法的方法来逼近这类地图的不动点。实际上，我们将通过递归公式xn+i= kn+ if （xn）生成一个序列{xn}，其中，φ是所讨论的映射，{kn}是实数序列。我们的主要结果是定理3，它给出了在kn上保证xn强收敛于不动点f的充分条件。
Introduction. This paper is concerned with nonexpanding maps from the unit ball of a real Hubert space into itself. Browder [l] has established that such maps always possess at least one fixed point. We shall develop a method, which resembles the simple iterative method, for approximating fixed points of such maps. In fact, we shall generate a sequence,{xn}, by the recursive formula xn+i= kn+ if (xn) where ƒ is the map in question and {kn} is a sequence of real numbers. Our main result is Theorem 3 which states sufficient conditions on kn to insure the strong convergence of xn to a fixed point of ƒ.