关于广义I型渐近拟非扩张映射的收敛定理-论文.pdf

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1、第31卷第1期苏州科技学院学报(自然科学版)Vo1．31No．12014年3月JournalofSuzhouUniversityofScienceandTechnology(NaturalScience)Mar．2014Convergencetheoremsforgeneralized／-asymptotically●quasi-，T■0■，■XIETao，GUOWeiping(SchooleofMathematicsandPhysics，SUST，Suzhou215009，China)XAbstract：Thispaperstudiesthesptrongcon

2、vergenceofgeneralized／-asymptoticallyquasi—nonexpansivemappingintheuniformlyconvexBanachspace．Aa，Tnd■wehaveobtainedsomestrongconvergencetheoremsandasufficientlynecessarycondition．S●lKeywords：generalized，一asymptotica1lyquasi-nonexpansivemapping；uniformlyconvexBanachspace；strongconver—V

3、gence；commonfixedpointe，YT■ChineseLibraryClassification：0177．9MR(2000)SubjectClassification：47H09；47H10LiteratureLabelCode：APaperNumber：l672—0687(2014)0l一0029—05ap1Introduction●lp，T■LetCbeanonemptysubsetgofarealBanachspaceEand：CCbeamapping．F(T)=∈C：Tx--~}denotesthesetoffixedpointsofDef

4、inition1tI-3】Amapping：Cissaidtobe(i)asympt0ticallynonexpansiveifthereexistsasequence{)≥lC[1，∞)withlim=1suchthatn—+∞—I】≤ll—，，II，V，Y∈C，n≥1(ii)uniformlyL—LipschitzianifthereexistsaconstantL>0satisfying—【I≤llx-ylI，V，Y∈C，n≥l(iii)semi—compactifCisclosedandforanyboundedsequence{．q'fnl≥linCwi

5、thlimll9On一ll=0，theren—叶∞existasubsequence(}≥Ic_{}≥1and∈Csuchthatlira=．E—_+cDefinition2【4】Amapping：CCissaidtobeasymptoticallyquasi-nonexpansiveifthereexistsasequence{A)】c[0，。。)withliraA0andF(T)≠suchthat，r∞ll7_Pll≤(I+A)ll_pII，Yx∈C，n≥1andP∈F(T)Definition3LetTI：CCbetwomappings．Tiscalled(

6、i)I-nonexpansiveonCif[收稿日期】2012—12—20[基金项目]国家自然科学基金资助项目(11271282)[作者简介]谢涛(1986一)，男，江苏溧阳人，硕士研究生，研究方向：泛函分析。30苏州科技学院学报(自然科学版)2014．缸ll一lI≤ll一ll，V，Y∈C(ii)嘲／-asymptoticallynonexpansiveonCifthereexistsasequence{AlC[0，∞)withlimAIJ，=Osuchthat一∞lIT'x-T'yII≤(I+A，)JIt'x-ryfjf0rall，Y∈Candn=l，2⋯，(i

7、ii)l-asymptoticallyquasi—nonexpansiveonCifthereexistsasequence{AJc[o，∞)withlimA，，=0and，r—’∞F=F(T)nF(I)≠0suchthatlJll≤(1+a，)Illf_0rall∈CandP∈，()nF(I)andn=l，2，⋯(iv)generalizedI-asympt。ticallyquasi—nonexpansivemappingif，：F(71)nF(I)≠andthereexistsequencesofrealnumbers{“)，{，}withlimu．=lim，

8、=Osuc