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


Iterative approximation of fixed points of Lipschitzian strictly pseudocontractive mappings

Author: C. E. Chidume
Journal: Proc. Amer. Math. Soc. 99 (1987), 283-288
MSC: Primary 47H10; Secondary 47H09
MathSciNet review: 870786
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Abstract: Suppose $ X = {L_p}({\text{or}}\;{l_p}),p \geq 2$, and $ K$ is a nonempty closed convex bounded subset of $ X$. Suppose $ T:K \to K$ is a Lipschitzian strictly pseudo-contractive mapping of $ K$ into itself. Let $ \{ {C_n}\} _{n = 0}^\infty $ be a real sequence satisfying:

(i) $ 0 < {C_n} < 1$ for all $ n \geq 1$,

(ii) $ \sum\nolimits_{n = 1}^\infty {{C_n} = \infty } $, and

(iii) $ \sum\nolimits_{n = 1}^\infty {C_n^2 < \infty } $.

Then the iteration process, $ {x_0} \in K$,

$\displaystyle {x_{n + 1}} = (1 - {C_n}){x_n} + {C_n}T{x_n}$

for $ n \geq 1$, converges strongly to a fixed point of $ T$ in $ K$.

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PII: S 0002-9939(1987)0870786-4
Article copyright: © Copyright 1987 American Mathematical Society

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