简介：Inthisstudy,weuseinexactnewtonmethodstofindsolutionsofnonlinear,nondifferenti-ableoperatorequationsonBanachspaceswithaconvergencestructure.ThistechniqueinvolvestheintroductionofageneralizednormasanoperatorfromalinearspaceintoapartiallyorderedBanachspace.Inthiswaythemetricpropertiesoftheexaminedproblemcanbeanalyzedmoreprecisely.Moreover,thisapproachallmvsustoderivefromthesametheorem,ontheonehand,semi-localresultsofKantorovich-type,andontheotherhand,globalresultsbasedonmono-tonicityconsiderations.Furthermore,iveshowthatspecialcasesofourresultsreducetothecorrespondingonesalreadyintheliterature.Finally>ourresultsareusedtosolveintegralequationsthatcannotbesolvedwithexistingmethods.

简介：Inthispaper,theapproximationproblemsofIshikawaiterationwitherrorsoffixedpointsforasymptoticallynonexpansivemappingsandasymptoticallypseudocontractivemappingsinarbitraryrealBanachspacesareinvestigated.Somenecessaryconditionandsufficientconditionfortheconvergenceofiterativesequencesaregivenrespectively.Theresultsthusextendandimprovesomerecentcorrespondingresults.

简介：TheexistenceofsolutionsforsystemsofnonlinearimpulsiveVolterraintegralequationsontheinfiniteintervalR+withaninfinitenumberofmomentsofimpulseeffectinBanachspacesisstudied.Someexistencetheoremsofextremalsolutionsareobtained,whichextendtherelatedresultsforthisclassofequationsonafiniteintervalwithafinitenumberofmomentsofimpulseeffect.Theresultsaredemonstratedbymeansofanexampleofaninfinitesystemsforimpulsiveintegralequations.

简介：Weshallgeneralizetheresultsof[9]aboutcharacterizationofisomorphismsonquasi-Banachalgebrasbyprovidingintegraltypeconditions.Also,weshallgivesomenewresultsinthiswayandfinally,givearesultabouthybridfixedpointoftwohomomorphismsonquasi-Banachalgebras.

简介：Inthispaper,wearedevotedtotheconvergenceanalysisofalgorithmsforgeneralizedset-valuedvariationalinclusionsinBanachspaces.Ourresultsimprove,extend,anddeveloptheearlierandrecentcorrespondingresults.

简介：ＴＨＥＰＡＴＨＷＩＳＥＳＯＬＵＴＩＯＮＦＯＲＡＣＬＡＳＳＯＦＱＵＡＳＩＬＩＮＥＡＲＳＴＯＣＨＡＳＴＩＣＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＩＮＢＡＮＡＣＨＳＰＡＣＥＳＩＨｕＹａｏｚｈｏｎｇ（胡耀忠）（ＷｕｈａｎＩｎｓｔ．ｏｆＭａｔｈ．Ｓｃｉ．，Ｃ...

简介：LetB(resp.K,Bl,Kl)denotethesetofallnonemptybounded(resp.compact,boundedconvex,compactconvex)closedsubsetsoftheBanachspaceX,endowedwiththeHausdorffmetric,andletGbeanonemptyrelativelyweaklycompactclosedsubsetofX.LetB°standforthesetofallF∈Bsuchthattheproblem(F,G)iswell-posed.Weprovedthat,ifXisstrictlyconvexandKadec,thesetKl∩B°isadenseG_δ-subsetofKl\G.Furthermore,ifXisauniformlyconvexBanachspace,wewillprovemore,namelythatthesetB\B°(resp.K\B°,Bl\B°,Kl\B°)isa-porousinB(resp.K,Bl,Kl).Moreover,weprovethatformost(inthesenseoftheBairecategory)closedboundedsubsetsGofX,thesetK\B°isdenseanduncountableinK.

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简介：Inthisarticle,wewillinvestigatethepropertiesofiterativesequencefornon-expansivemappingsandpresentseveralstrongandweakconvergenceresultsofsuccessiveapproximationstofixedpointsofnon-expansivemappingsinuniformlyconvexBanachspaces.Theresultspresentedinthisarticlegeneralizeandimprovevariousonesconcernedwithconstructivetechniquesforthefixedpointsofnon-expansivemappings.

简介：在一致凸Banach空间上，研究了半紧的非扩张压缩映象｜｜Tx-Ty｜｜≤｜｜x-y｜｜的Ishikawa型的三重迭代序列的收敛性问题，建立并证明了带误差的Ishikawa三重迭代逼近收敛定理，从而独特的推广了Mann和Ishikawa迭代方法，改进和发展了文献[1]-[7]的主要结果．

简介：WeextendtheconceptofframemultiresolutionanalysistoalocallycompactabeliangroupanduseittodefinecertainweightedBanachspacesandthespacesoftheirantifunctionals.Wedefineanalysisandsynthesisoperatorsonthesespacesandestablishthecontinuityoftheircomposition.Also,weproveageneralresulttocharacterizeinfinitetreesintheaboveBanachspacesofantifunctionals.ThispaperpavesthewayforthestudyofcorrespondingproblemsassociatedwithsomeothertypesofBanachspacesonlocallycompactabeliangroupsincludingmodulationspaces.

简介：Inthispaper,westudyanoperatorswhichmapseveryn-by-nsymmetricmatrixA,toamatrixs(A_n)thatminimizes||B_n-A_n||FoverthesetofallmatricesB_n,thatcanbediagonalizedbythesinetransform.Thematrixs(A_n),calledtheoptimalsinetransformpreconditioner,isdefinedforanyn-by-nsymmetricmatricesA_n.Thecostofconstructings(A_n)isthesameasthatofoptimalcirculantpreconditionerc(A_n)whichisdefinedin[8],Thes(A_n)hasbeenprovedin[6]tobeagoodpreconditionerinsolvingsymmetricToeplitzsystemswiththepreconditionedconjugategradient(PCG)method.Inthispaper,wediscussthealgebraicandgeometricpropertiesoftheoperators,andcomputeitsoperatornormsinBanachspacesofsymmetricmatrices.Somenumericaltestsandanapplicationinimagerestorationarealsogiven.

简介：TheconvergenceproblemofthefamilyofEuler-HalleymethodsisconsideredundertheLipschitzconditionwiththeL-average,andaunitedconvergencetheorywithitsapplicationsispresented.

简介：InthepresentpaperweintroducearandomiterationschemeforthreerandomoperatorsdefinedonaclosedandconvexsubsetofauniformlyconvexBanachspaceandproveitsconvergencetoacommonfixedpointofthreerandomoperators.Theresultisalsoanextensionofaknowntheoreminthecorrespondingnon-randomcase.

简介：

简介：AnewclassofalmostasymptoticallynonexpansivetypemappingsinBanachspacesisintroduced,whichincludesanumberofknownclassesofnonlinearLipschitzianmappingsandnon-LipschitzianmappingsinBanachspacesasspecialcases;forexample,theknownclassesofnonexpansivemappings,asymptoticallynonexpansivemappingsandasymptoticallynonexpansivetypemappings.TheconvergenceproblemofmodifiedIshikawaiterativesequenceswitherrorsforapproximatingfixedpointsofalmostasymptoticallynonexpansivetypemappingsisconsidered.NotonlyS.S.Chang'sinequalitybutalsoH.K.Xu'soneforthenormsofBanachspacesareappliedtomaketheerrorestimatebetweentheexactfixedpointandtheapproximateone.Moreover,ZhangShi-sheng'smethod(AppliedMathematicsandMechanics(EnglishEdition),2001,22(1):25-34)formakingtheconvergenceanalysisofmodifiedIshikawaiterativesequenceswitherrorsisextendedtothecaseofalmostasymptoticallynonexpansivetypemappings.ThenewconvergencecriteriaofmodifiedIshikawaiterativesequenceswitherrorsforfindingfixedpointsofalmostasymptoticallynonexpansivetypemappingsinuniformlyconvexBanachspacesarepresented.Also,thenewconvergencecriteriaofmodifiedManniterativesequenceswitherrorsforthisclassofmappingsareimmediatelyobtainedfromthesecriteria.Theaboveresultsunify,improveandgeneralizeZhangShi-sheng'sonesonapproximatingfixedpointsofasymptoticallynonexpansivetypemappingsbythemodifiedIshikawaandManniterativesequenceswitherrors.

简介：WeprovethatforeveryLipschitzisomorphismffromaseparableHilbertspaceHtoaBanachspaceYwithRadon-Nikodymproperty,thereisaboundedsurjectivelinearoperatorT:H→Ysothat(f+T)-1(NG(f-1))isaΓ-nullsetofH,whereNG(f-1)isthesetofallthepointsofGteauxnon-differentiabilityoff-1.

简介：在本文中,我们定义和研究了I0Rm到Banach空间X中函数的强McShane积分,直接证明了强Mcshane积分与Bochner积分是等价的,McShane积分与强Mcshane积分等价当且仅当Banach空间X有限维.从而部分地回答了R.A.Gordon的一个公开问题.

简介：在这篇论文，我们在与下列PexiderizedJensen功能的方程联系的quasi-Banach代数学证明同形的概括Hyers-Ulam稳定性这被用于调查在quasi-Banach代数学之间的同形。概括Hyers-Ulam稳定性的概念从Rassia出现在他的纸的稳定性定理发源：在在Banach空格的线性印射的稳定性上，Proc。Amer。数学。Soc，72，297300(1978)。

简介：WestudytheboundedandthecompactweightedcompositionoperatorsfromtheBlochspaceintotheweightedBanachspacesofholomorphicfunctionsonboundedhomogeneousdomains,withparticularattentiontotheunitpolydisk.Forboundedhomogeneousdomains,wecharacterizetheboundedweightedcompositionoperatorsanddeterminetheoperatornorm.Inaddition,weprovidesufficientconditionsforcompactness.Fortheunitpolydisk,wecompletelycharacterizethecompactweightedcompositionoperators,aswellasprovide'computable'estimatesontheoperatornorm.