Strong Convergence of Viscosity Approximation Methods for Nonexpansive Mappings in CAT(0) Spaces
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-06-10
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces are studied.
Consider a nonexpansive self-mapping T of a closed convex subset C of a CAT(0) space X.
Suppose that the set Fix(T) of fixed points of T is nonempty.
For a contraction f on C and t∈(0,1), let xt∈C be the unique fixed point of the contraction x↦tf(x)⊕(1-t)Tx.
We will show that if X is a CAT(0) space satisfying some property, then {xt} converge strongly to a fixed point of T which solves some variational inequality.
Consider also the iteration process {xn}, where x0∈C is arbitrary and xn+1=αnf(xn)⊕(1-αn)Txn for n≥1, where {αn}⊂(0,1).
It is shown that under certain appropriate conditions on αn,{xn} converge strongly to a fixed point of T which solves some variational inequality.
American Psychological Association (APA)
Shi, Luo Yi& Chen, Ru Dong. 2012. Strong Convergence of Viscosity Approximation Methods for Nonexpansive Mappings in CAT(0) Spaces. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-993246
Modern Language Association (MLA)
Shi, Luo Yi& Chen, Ru Dong. Strong Convergence of Viscosity Approximation Methods for Nonexpansive Mappings in CAT(0) Spaces. Journal of Applied Mathematics No. 2012 (2012), pp.1-11.
https://search.emarefa.net/detail/BIM-993246
American Medical Association (AMA)
Shi, Luo Yi& Chen, Ru Dong. Strong Convergence of Viscosity Approximation Methods for Nonexpansive Mappings in CAT(0) Spaces. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-993246
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993246