FIXED-POINT THEOREMS FOR NON-LIPSCHITZIAN MAPPINGS OF ASYMPTOTICALLY NONEXPANSIVE TYPE
FIXED-POINT THEOREMS FOR NON-LIPSCHITZIAN MAPPINGS OF ASYMPTOTICALLY NONEXPANSIVE TYPE
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DOI：
10.1007/bf02757136
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发表时间：
1974-01-01
影响因子：
1
通讯作者：
KIRK, WA
中科院分区：
文献类型：
--
作者：
KIRK, WA
LetXbe a Banach space,Ka nonempty, bounded, closed and convex subset ofX, and supposeT:K→Ksatisfies: for eachx∈K, lim supi→∞{supy∈K‖tix−Tiy∼−‖x−y‖}≦0. IfTNis continuous for some positive integerN, and if either (a)Xis uniformly convex, or (b)Kis compact, thenThas a fixed point inK. The former generalizes a theorem of Goebel and Kirk for asymptotically nonexpansive mappings. These are mappingsT:K→Ksatisfying, forisufficiently large, ‖Tix−Tiy‖≦ki‖x−y∼,x,y∈K, whereki→1 asi→∞. The precise assumption in (a) is somewhat weaker than uniform convexity, requiring only that Goebel’s characteristic of convexity, ɛ0(X), be less than one.
