Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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$.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H10, 47H09

Retrieve articles in all journals with MSC: 47H10, 47H09


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0870786-4
PII: S 0002-9939(1987)0870786-4
Article copyright: © Copyright 1987 American Mathematical Society