非列紧空间的一般非扩张映象的Ishikawa迭代序列

THE SEQUECE OF ISHIKAWA ITERATES FOR GENERALIZEDNONEXPANSIVE MAPPING IN NONCOMPACT SPACE

本文证明了Hilbert空间上的非列紧的一般非扩张映象的Ishikawa迭代序列的收敛性。

Let C be a nonempty convex subset of a normed linear space.For,each x0∈C.the iteration sequence is called an ishikawa scheme if and {αn} {βn} satisfy (i)In this paper we have proved following theorem.Theorem Let C be a closed convex nonempty bounded subset of a Hilbert space and T;C→C a continuous generalizednonexpansive demicompact mapping with F(T) nonempty. Then, for each x0→C sequence of Ishikawa iterates converges to a fixed point of T.