渐近半伪压缩映射的强收敛的充分必要条件.pdfVIP

数 学 杂 志 Vo1．35(2015) No．4 J．ofMath．(PRC) A SUFFICIENT AND NECESSARY C0NDITION F0R THE STR0NG C0NVERGENCE 0F ASYM PToTICALLY HEM I—PSEUDoNTRACTIVE M APPING LIU Yong—quan，GUO W ei—ping (SchoolofMathematicsandPhysics，SuzhouUniversityofScienceandTechnology， Suzhou215009,China) Abstract：In thispaper，theasymptotically hemi—pseudocontractivemappingisstudied in Banach space．Byusingthemodified Ishikawaiterativeschemewith errors．someSU币cientand necessary conditionsonthestrongconvergenceforapproximationoffixedpointsoftheuniformly L—Lipschitzian asymptoticallyhemi—pseudocontractivemappingareobtained，which extend and improvesomecorrespondingresults． Keywords： fixedpoint；Banachspace；asymptoticallypseudocontractivemapping；asymp— toticallyhemi--pseudocontractivemapping；uniformlyL--Lipshitzianmapping 2010MR SubjectClassification： 47H09；47J05 Documentcode： A ArticleID： 0255-7797(2015)04—0747—07 1 Introduction and Prelim inaries Throughoutthiswork，weassumethatE isarealBanachspace，E isthedualspace ofE andJ ：E _ 2E isthenormalizeddualitymappingdefinedby J(5)={t厂∈E ：(5，f)=I151… ，1IflI：11511)，Vx∈E， where(·，)·denotesdualitypairingbetweenEandE ．Asingle—valuednormalizedduality mappingisdenotedbyJ． LetC beanonemptysubsetofE andT ：C Crbeamapping．W edenotethesetof fixedpointsofTbyF()，i．e．，F(T)= 5∈C：Tx= )． Definition1．1(1)(see[1])Tissaidtobepseud0contractive，ifforallx，Y∈C，there existsj(x—Y)∈J(～Y)suchthat(Tx—Ty，j(5一 )) IIx一 lf． (2)(see[2])TissaidtobeuniformlyL—LipshitzianifthereexistsL0suchthat T5～T lISLIIx一 Receiveddate：2013一Ol一02 Accepteddate：2013—05．30 Foundationitem：Supporte