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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
DOI: https://doi.org/10.1090/S0002-9939-1987-0870786-4
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, ${x_0} \in K$, \[ {x_{n + 1}} = (1 - {C_n}){x_n} + {C_n}T{x_n}\] for $n \geq 1$, converges strongly to a fixed point of $T$ in $K$.


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Article copyright: © Copyright 1987 American Mathematical Society