关于Lipschitzian伪压缩映射的合成隐迭代序列(英文).pdf

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1、数学杂志Vo1.34(2014)NO.1!:皇:(2CoMPoSITEIMPLICITITERATIoNPRoCESSFoRALIPSCHITZIANPSEUDoC0NTRACTIVEMAPPINGKANXu—zhou,GUOWei—ping(SchoolofMathematicsandPhysics,SuzhouUniversityofScienceandTechn0l0夕,Suzhou215009,China)Abstract:Inthispaper,thecompositeimplicititerativeprocess

2、foraLipschitzianpseudocon—tractivemappingisstudied.Byusingthecorrespondingequivalentinequalityofpseudocontractivemapping,thesuficientandnecessaryconditionsforthestrongconvergenceofthecompositeim—plicititerativeprocessareobtainedinBanachspaces,whichgeneralizesomerela

3、tedresults.Keywords:pseud0contractivemapping;fixedpoint;compositeimplicititerativescheme;Banachspace2010MRSubjectClassification:47H09;47J05;47J25Documentcode:AArticleID:0255—7797(2014)0l一0001.061IntroductionandPreliminariesThroughoutthiswork,weassumethatEisarealBana

4、chspace,EisthedualspaceofEandJ:E-_+2EisthenormalizeddualitymappingdefinedbyJ(x)={,∈E:(X,f)=IIxlllIfll,IIfll=IIxll},Vx∈E,where(’,‘)denotesdualitypairingbetweenEandE.Asingle—valuednormalizeddualitymappingisdenotedbyJ.LetCbeanonemptysubsetofE,T:Cbeamapping.Wedenotethes

5、etoffixedpointsofTbyF().AmappingTwithdomainD(T)andrangeR(T)inEiscalledpseudocontractive『1],ifthereexistssomej(x—Y)∈J(x—Y)suchthat(j(x一),Tx—Ty)JIx一ll。f0rall,Y∈D(T).Itiswellknownthat[2](1.1)isequivalenttothe~llowingIl一J『IIx—Y+s[(,一T)x一(一T)y]ll(1.2)f0ralls>0andall,Y∈D(

6、).Receiveddate:2012—10—12Accepteddate:2012—12—24Foundationitem:SupportedbyNationalNaturalScienceFoundationofChina(11271282).Biography:KanXuzhou(1985~),male,bornatBengbu,Anhui,master,majorinnonlinearfunctionalanalysis.2JournalofMathematicsVo1.34Theorem1.1[3]LetCbeaco

7、nvexcompactsubsetofaHilbertspace日andT:C_CbeaLipschitzianpseudocontractivemapping.Foranyl∈C,supposethesequence{n)isdefinedby{l=(1~)+麦,’⋯n1,、3where{),{)aretworealsequencesin[0,1]satisfying(i),n1;(ii)lim=0;(iii)∑l=∞.Then{n}convergesstronglytoafixedpointofT.Remark1.1(1)

8、Since0l,rt1and2n%1=。。,theiterativesequence(1.3)couldn’tbereducedtoManniterativesequencebysetting=0.TheManniterativesequence[4]isdefinedbyt

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《关于Lipschitzian伪压缩映射的合成隐迭代序列(英文).pdf》由会员上传分享,免费在线阅读,更多相关内容在行业资料-天天文库

1、数学杂志Vo1.34(2014)NO.1!:皇:(2CoMPoSITEIMPLICITITERATIoNPRoCESSFoRALIPSCHITZIANPSEUDoC0NTRACTIVEMAPPINGKANXu—zhou,GUOWei—ping(SchoolofMathematicsandPhysics,SuzhouUniversityofScienceandTechn0l0夕,Suzhou215009,China)Abstract:Inthispaper,thecompositeimplicititerativeprocess

2、foraLipschitzianpseudocon—tractivemappingisstudied.Byusingthecorrespondingequivalentinequalityofpseudocontractivemapping,thesuficientandnecessaryconditionsforthestrongconvergenceofthecompositeim—plicititerativeprocessareobtainedinBanachspaces,whichgeneralizesomerela

3、tedresults.Keywords:pseud0contractivemapping;fixedpoint;compositeimplicititerativescheme;Banachspace2010MRSubjectClassification:47H09;47J05;47J25Documentcode:AArticleID:0255—7797(2014)0l一0001.061IntroductionandPreliminariesThroughoutthiswork,weassumethatEisarealBana

4、chspace,EisthedualspaceofEandJ:E-_+2EisthenormalizeddualitymappingdefinedbyJ(x)={,∈E:(X,f)=IIxlllIfll,IIfll=IIxll},Vx∈E,where(’,‘)denotesdualitypairingbetweenEandE.Asingle—valuednormalizeddualitymappingisdenotedbyJ.LetCbeanonemptysubsetofE,T:Cbeamapping.Wedenotethes

5、etoffixedpointsofTbyF().AmappingTwithdomainD(T)andrangeR(T)inEiscalledpseudocontractive『1],ifthereexistssomej(x—Y)∈J(x—Y)suchthat(j(x一),Tx—Ty)JIx一ll。f0rall,Y∈D(T).Itiswellknownthat[2](1.1)isequivalenttothe~llowingIl一J『IIx—Y+s[(,一T)x一(一T)y]ll(1.2)f0ralls>0andall,Y∈D(

6、).Receiveddate:2012—10—12Accepteddate:2012—12—24Foundationitem:SupportedbyNationalNaturalScienceFoundationofChina(11271282).Biography:KanXuzhou(1985~),male,bornatBengbu,Anhui,master,majorinnonlinearfunctionalanalysis.2JournalofMathematicsVo1.34Theorem1.1[3]LetCbeaco

7、nvexcompactsubsetofaHilbertspace日andT:C_CbeaLipschitzianpseudocontractivemapping.Foranyl∈C,supposethesequence{n)isdefinedby{l=(1~)+麦,’⋯n1,、3where{),{)aretworealsequencesin[0,1]satisfying(i),n1;(ii)lim=0;(iii)∑l=∞.Then{n}convergesstronglytoafixedpointofT.Remark1.1(1)

8、Since0l,rt1and2n%1=。。,theiterativesequence(1.3)couldn’tbereducedtoManniterativesequencebysetting=0.TheManniterativesequence[4]isdefinedbyt

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