Full Text:
<3130>
CLC number: O177.91
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 0000-00-00
Cited: 2
Clicked: 5359
Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings
| |||||||||||||
WANG Ya-qin. Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings[J]. Journal of Zhejiang University Science A, 2007, 8(10): 1691-1694.
@article{title="Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings",
author="WANG Ya-qin",
journal="Journal of Zhejiang University Science A",
volume="8",
number="10",
pages="1691-1694",
year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A1691"
}
%0 Journal Article
%T Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings
%A WANG Ya-qin
%J Journal of Zhejiang University SCIENCE A
%V 8
%N 10
%P 1691-1694
%@ 1673-565X
%D 2007
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A1691
TY - JOUR
T1 - Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings
A1 - WANG Ya-qin
J0 - Journal of Zhejiang University Science A
VL - 8
IS - 10
SP - 1691
EP - 1694
%@ 1673-565X
Y1 - 2007
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2007.A1691
Abstract: Let K be a closed convex subset of a real reflexive Banach space E, T:K→K be a nonexpansive mapping, and f:K→K be a fixed weakly contractive (may not be contractive) mapping. Then for any t∈(0, 1), let xt(K be the unique fixed point of the weak contraction x↦tf(x)+(1−t)Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E*, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in (Xu, 2004).
[1] Alber, Y.I., Guerre-Delabriere, S., 1997. Principle of weakly contractive maps in Hilbert spaces. Operator Theory, Advances and Applications, 98:7-22.
[2] Chen, R.D., Song, Y.S., Zhou, H.Y., 2006. Viscosity approximation methods for continuous pseudocontractive mappings. Acta Math. Sinica (Chinese Series), 49(6):1275-1278.
[3] Gossez, J.P., Lami Dozo, E., 1972. Some geometric properties related to the fixed point theory for nonexpansive mapping. Pacific J. Math., 40:565-573.
[4] Jung, J.S., 2005. Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces. J. Math. Anal. Appl., 302:509-520.
[5] Rhoades, B.E., 2001. Some theorems on weakly contractive maps. Nonl. Anal., 47:2683-2693.
[6] Song, Y.S., Chen, R.D., 2007. Convergence theorems of iterative algorithms for continuous pseudocontractive mappings. Nonl. Anal.: Theory, Methods & Appl., 67(2):486-497.
[7] Xu, H.K., 2004. Viscosity approximation methods for nonexpansive mappings. J. Math. Anal. Appl., 298:279-291.
Open peer comments: Debate/Discuss/Question/Opinion
<1>