An Iteration Method for Nonexpansive Mappings in Hilbert Spaces
In real Hilbert space H, from an arbitrary initial point x0∈H, an explicit iteration scheme is defined as follows: xn+1=αnxn+(1−αn)Tλn+1xn,n≥0, where Tλn+1xn=Txn−λn+1μF(Txn), T:H→H is a nonexpansive mapping such that F(T)={x∈K:Tx=x} is nonempty, F:HâÂ...
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2006-12-01
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Series: | Fixed Point Theory and Applications |
Online Access: | http://dx.doi.org/10.1155/2007/28619 |
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doaj-fa92c51876624cc4acfd2fda225497552020-11-24T20:51:44ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122006-12-01200710.1155/2007/28619An Iteration Method for Nonexpansive Mappings in Hilbert SpacesLin WangIn real Hilbert space H, from an arbitrary initial point x0∈H, an explicit iteration scheme is defined as follows: xn+1=αnxn+(1−αn)Tλn+1xn,n≥0, where Tλn+1xn=Txn−λn+1μF(Txn), T:H→H is a nonexpansive mapping such that F(T)={x∈K:Tx=x} is nonempty, F:H→H is a η-strongly monotone and k-Lipschitzian mapping, {αn}⊂(0,1), and {λn}⊂[0,1). Under some suitable conditions, the sequence {xn} is shown to converge strongly to a fixed point of T and the necessary and sufficient conditions that {xn} converges strongly to a fixed point of T are obtained.http://dx.doi.org/10.1155/2007/28619 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Lin Wang |
spellingShingle |
Lin Wang An Iteration Method for Nonexpansive Mappings in Hilbert Spaces Fixed Point Theory and Applications |
author_facet |
Lin Wang |
author_sort |
Lin Wang |
title |
An Iteration Method for Nonexpansive Mappings in Hilbert Spaces |
title_short |
An Iteration Method for Nonexpansive Mappings in Hilbert Spaces |
title_full |
An Iteration Method for Nonexpansive Mappings in Hilbert Spaces |
title_fullStr |
An Iteration Method for Nonexpansive Mappings in Hilbert Spaces |
title_full_unstemmed |
An Iteration Method for Nonexpansive Mappings in Hilbert Spaces |
title_sort |
iteration method for nonexpansive mappings in hilbert spaces |
publisher |
SpringerOpen |
series |
Fixed Point Theory and Applications |
issn |
1687-1820 1687-1812 |
publishDate |
2006-12-01 |
description |
In real Hilbert space H, from an arbitrary initial point x0∈H, an explicit iteration scheme is defined as follows: xn+1=αnxn+(1−αn)Tλn+1xn,n≥0, where Tλn+1xn=Txn−λn+1μF(Txn), T:H→H is a nonexpansive mapping such that F(T)={x∈K:Tx=x} is nonempty, F:H→H is a η-strongly monotone and k-Lipschitzian mapping, {αn}⊂(0,1), and {λn}⊂[0,1). Under some suitable conditions, the sequence {xn} is shown to converge strongly to a fixed point of T and the necessary and sufficient conditions that {xn} converges strongly to a fixed point of T are obtained. |
url |
http://dx.doi.org/10.1155/2007/28619 |
work_keys_str_mv |
AT linwang aniterationmethodfornonexpansivemappingsinhilbertspaces AT linwang iterationmethodfornonexpansivemappingsinhilbertspaces |
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