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Received: 2007-04-20

Revision Accepted: 2007-06-22

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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.12 P.2032-2036

http://doi.org/10.1631/jzus.2007.A2032


Weak and strong convergence of an explicit iteration scheme with perturbed mapping for nonexpansive mappings


Author(s):  WANG Ya-qin

Affiliation(s):  Mathematics and Sciences College, Shanghai Normal University, Shanghai 200234, China

Corresponding email(s):   wangyaqin0579@126.com

Key Words:  Nonexpansive mapping, Iteration scheme with perturbed mapping, Opial condition, Completely continuous


WANG Ya-qin. Weak and strong convergence of an explicit iteration scheme with perturbed mapping for nonexpansive mappings[J]. Journal of Zhejiang University Science A, 2007, 8(12): 2032-2036.

@article{title="Weak and strong convergence of an explicit iteration scheme with perturbed mapping for nonexpansive mappings",
author="WANG Ya-qin",
journal="Journal of Zhejiang University Science A",
volume="8",
number="12",
pages="2032-2036",
year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A2032"
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%T Weak and strong convergence of an explicit iteration scheme with perturbed mapping for nonexpansive mappings
%A WANG Ya-qin
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%@ 1673-565X
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A2032

TY - JOUR
T1 - Weak and strong convergence of an explicit iteration scheme with perturbed mapping for nonexpansive mappings
A1 - WANG Ya-qin
J0 - Journal of Zhejiang University Science A
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SP - 2032
EP - 2036
%@ 1673-565X
Y1 - 2007
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2007.A2032


Abstract: 
In this paper, we consider an explicit iteration scheme with perturbed mapping for nonexpansive mappings in real q-uniformly smooth Banach spaces. Some weak and strong convergence theorems for this explicit iteration scheme are established. In particular, necessary and sufficient conditions for strong convergence of this explicit iteration scheme are obtained. At last, some useful corollaries for strong convergence of this explicit iteration scheme are given.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Jung, J.S., 2005. Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces. J. Math. Anal. Appl., 302:509-520.

[2] Maiti, M., Ghosh, M.K., 1989. Approximating fixed points by Ishikawa iterates. Bull. Aust. Math. Soc., 40(1):113-117.

[3] Osilike, M.O., Aniagbosor, S.C., Akuchu, B.G., 2002. Fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces. Pan-Amer. Math. J., 12:77-88.

[4] Senter, H.F., Dotson, W.G.Jr., 1974. Approximating fixed points of nonexpansive mappings. Proc. Amer. Math. Soc., 44(2):375-380.

[5] Suzuki, T., 2005. Strong convergence of Krasnoselskii and Mann’s type sequences for one-parameter nonexpansive semigroups without Bochner integrals. J. Math. Anal. Appl., 305(1):227-239.

[6] Tan, K.K., Xu, H.K., 1993. Approximating fixed points of nonexpansive mappings by the Ishikawa iterative process. J. Math. Anal. Appl., 178:301-308.

[7] Wang, L., 2007. An iteration method for nonexpansive mappings in Hilbert spaces. Fixed Point Theory and Applications, in press.

[8] Xu, H.K., 1991. Inequalities in Banach spaces with applications. Nonl. Anal., 16(12):1127-1138.

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