Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space

Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space

Let C be nonempty closed convex subset of real Hilbert space H. Consider C a nonexpansive semigroup ℑ={T(s):s≥0} with a common fixed point, a contraction f with coefficient 0<α<1, and a strongly positive linear bounded operator A with coefficient γ¯>0. Let 0<γ<Î...

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Main Authors: Yongfu Su, Suhong Li, Lihua Li
Format: Article
Language:English
Published: SpringerOpen 2008-11-01
Series:Fixed Point Theory and Applications
Online Access:http://dx.doi.org/10.1155/2008/484050
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spelling doaj-a674fc5698b4465ab41e58de9536905b2020-11-24T20:51:43ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122008-11-01200810.1155/2008/484050Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert SpaceYongfu SuSuhong LiLihua LiLet C be nonempty closed convex subset of real Hilbert space H. Consider C a nonexpansive semigroup ℑ={T(s):s≥0} with a common fixed point, a contraction f with coefficient 0<α<1, and a strongly positive linear bounded operator A with coefficient γ¯>0. Let 0<γ<γ¯/α. It is proved that the sequence {xn} generated iteratively by xn=(I−αnA)(1/tn)∫0tnT(s)ynds+αnγf(xn),yn=(I−βnA)xn+βnγf(xn) converges strongly to a common fixed point x∗∈F(ℑ) which solves the variational inequality 〈(γf−A)x∗,z−x∗〉≤0 for all z∈F(ℑ).http://dx.doi.org/10.1155/2008/484050
collection DOAJ
language English
format Article
sources DOAJ
author Yongfu Su
Suhong Li
Lihua Li
spellingShingle Yongfu Su
Suhong Li
Lihua Li
Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space
Fixed Point Theory and Applications
author_facet Yongfu Su
Suhong Li
Lihua Li
author_sort Yongfu Su
title Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space
title_short Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space
title_full Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space
title_fullStr Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space
title_full_unstemmed Composite Implicit General Iterative Process for a Nonexpansive Semigroup in Hilbert Space
title_sort composite implicit general iterative process for a nonexpansive semigroup in hilbert space
publisher SpringerOpen
series Fixed Point Theory and Applications
issn 1687-1820
1687-1812
publishDate 2008-11-01
description Let C be nonempty closed convex subset of real Hilbert space H. Consider C a nonexpansive semigroup ℑ={T(s):s≥0} with a common fixed point, a contraction f with coefficient 0<α<1, and a strongly positive linear bounded operator A with coefficient γ¯>0. Let 0<γ<γ¯/α. It is proved that the sequence {xn} generated iteratively by xn=(I−αnA)(1/tn)∫0tnT(s)ynds+αnγf(xn),yn=(I−βnA)xn+βnγf(xn) converges strongly to a common fixed point x∗∈F(ℑ) which solves the variational inequality 〈(γf−A)x∗,z−x∗〉≤0 for all z∈F(ℑ).
url http://dx.doi.org/10.1155/2008/484050
work_keys_str_mv AT yongfusu compositeimplicitgeneraliterativeprocessforanonexpansivesemigroupinhilbertspace
AT suhongli compositeimplicitgeneraliterativeprocessforanonexpansivesemigroupinhilbertspace
AT lihuali compositeimplicitgeneraliterativeprocessforanonexpansivesemigroupinhilbertspace
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