一类非紧算子的不动点.pdfVIP

维普资讯 第5卷第 3期 应用泛 函分析学报 Vo1．5 No．3 ACTA ANALYSIS FUNCTIONAIIS APPLICATA Sep．． 2003 2003年 9月 文章 编号 ：1009—1327 (2003)03—0231—03 Fixed PointsforNoncompactOperators GUO Lin DepartmentofMathematics，ChinaCoalEconomicCollage，YantaiShandong264005，China Abstract： Thispaperobtainssom enew andinteresttheorem on theexistenceoffixedpointsfor noncompactandnomonotoneoperators- Keywords： regularcone；fixedpoint；Zorn slemm a CLC number： O177．91 l IntrOductiOn IettherealBanachspaceE bepartiallyorderedbyaconeP ofE ，i．e． YifandonlyifY— ∈ P．ConeP issaidtobenormalifthereexistsapositiveconstantN such that0 z y impliesIl ll N llyll，where0denotesthezeroelementofE．Pissaidtoberegularifevery increasingandboundedinordersequenceinEhasalimit，i．e．if{z )∈Eandy∈Esatisfy l 2 … … Y，thenthereexists ∈Esuchthatl1z 一 I1 0，Pisregular impliesP isnorma1． In[1— 7]，theexistencetheorem offixedpointwasestablishedforcompactoperatoror monotone operator．Now，in this paper，we shalluse a different method to obtain some theoremson theexistenceoffixedpointsforoperatorA ，whichhasnocompactormonotone． Lemma O[](Zornslemma) LetF beanonemptypartially ordered setwith theproper thateverycompletelyorderedsubsetofFhasanupperbound inF．ThenF containsatleastone maximalelement． Lemma1[(Meanvaluetheorem) Let ()∈CEJ，E]，J一 [口，6]．Let Jand is countablesubsetofJ，ift∈ [日，6]＼F， (f)isdifferentiableatt，then (6)一 (日)∈ (6一a) ( (f)：t∈ ，6]＼ )． 2 M ain Theorem s LetA isanoperatorfrom E toE ，P isregulaeconeanda b，letuslistsomeconditionsfor lateruse (H )Aa三三=a，Ab b (H2)Aa a，Ab b (H3)in[口，6]，Ax z，thenthereexistz ，suchthatAx (H4)