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| ITERATION OF FIXED POINTS ON HYPERSPACES |
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Citation： |
Hu Thakyin,Huang Juichi.ITERATION OF FIXED POINTS ON HYPERSPACES[J].Chinese Annals of Mathematics B,1997,18(4):423~428 |
| Page view： 977
Net amount： 694 |
Authors： |
Hu Thakyin; Huang Juichi |
Foundation： |
the National Natural Science Foundation of China |
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| Abstract： |
Let $X$ be a compact, convex subset of a Banach space $E$ and
$CC(X)$ be the collection of all non-empty compact, coonvex
subset of $X$ equipped with the Hausdorff metric $h.$ Suppose
$\Cal K$ is a compact, convex subset of $CC(X)$ and $T:(\Cal K,
h)\to (\Cal K, h)$ is a nonexpansive mapping. Then for any
$A_0\in \Cal K,$ the sequence $\{ A_n\}$ defined by
$A_{n+1}=(A_n+TA_n)/2$ converges to a fixed point of $T.$ The
special case that $\Cal K$ consists of singletons only yields
results previously obtained by H. Schaefer, M. Edelstein and S.
Ishikawa respectively. |
Keywords： |
Iteration process, Fixed point, Hyperspace,Nonexpansive mapping |
Classification： |
47H10, 54B20 |
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