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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Approximation to fixed points of generalized nonexpansive mappings

Author: Chi Song Wong
Journal: Proc. Amer. Math. Soc. 54 (1976), 93-97
MathSciNet review: 0390850
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Abstract: Let $ K$ be a convex subset of a uniformly convex Banach space. It is proved that if $ K$ is compact, then the fixed points of a continuous generalized nonexpansive self-mapping $ T$ on $ K$ can be approximated by the iterates of $ {T_t}$ with $ t \in (0,1),{T_t}(x) = (1 - t)x + tT(x),x \in K;{T_t}$ is asymptotically regular if $ T$ has a fixed point.

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PII: S 0002-9939(1976)0390850-9
Article copyright: © Copyright 1976 American Mathematical Society