# Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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## Iterative approximation of fixed points of Lipschitzian strictly pseudocontractive mappingsHTML articles powered by AMS MathViewer

by C. E. Chidume
Proc. Amer. Math. Soc. 99 (1987), 283-288 Request permission

## 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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