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