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简介：本文考虑Banach空间中形如“=f(t,x,)(0≤t≤1),α_ix(i)+β_i(i)=ζ_i(i=0,1)”的边值问题,利用所谓γ—Lipshitz模数的概念得到这类边值问题的若干存在定理。

简介：利用Hahn-Banach延拓定理或与K-维体积相似的数给出了Banach空间K-严格凸的两个新的充要条件。

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：用不同于已有的方法证明了任意实Banach空间中一致Lipschitz强连接伪压缩算子在具误差的修正的Mann迭代和具误差的修正的Ishikawa迭代下收敛和稳定的等价性,其中迭代参数{βn}仅需limsupn→∞βn〈k/L（L＋1）,这推广和改进了目前需假设limn→∞βn=0和两迭代程序初始点的取值需相同条件下的已有结果.

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：通过不动点指数理论,讨论了一类超线性算子方程的多重解问题.在合适的条件下,我们至少得到了三个解:一个零解,一个正解和一个负解.并将抽象结果应用到超线性微分方程两点边值问题.

简介：通过一个反例,说明了欧氏空间中关于微分方程解的存在性的Peano定理,对Banach空间中微分方程是不成立的.并对Peano定理进行了改进,证明了改进后的结果在Banach空间中是成立的.

简介：推广了Banach空间中广义拟变分包含的概念，研究了无限族广义集值拟变分包含的解的存在性及其迭代逼近问题．所得结果改进和推广了一些最新的成果．

简介：在不要求C0-半群为紧半群的前提下．利用函数e^-λt（其中λ〉0是常数）和Monch不动点定理，在更广泛的条件下，得到了Banach空间中一类半线性混合型发展方程初值问题的整体mild解和正mild解，本质上改进和推广了已有相关结果．

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

简介：Inthispaper,letKbeanonemptysubsetofauniformlysmoothBanachspaceX,andT:K→2~kbeamultivaluedoperatorofthemonotonetype.TheiterativesequencewhichconvergesstronglytotheuniquefixedpointofTisgiven.OurresultsaretheextensionandimprovementsoftheresultsobtainedpreviouslybyseveralauthorsincludingDunn,Chidume,DengandDing.

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简介：文章利用正规对偶映射的定义，给出了任意Banach空间Lipschitz强伪压缩映射不动点的Ishikawa迭代收敛定理．该定理不仅推广了已知结果，而且还简化了目前相应结果的证明．

简介：深化对本性谱的认识;给出∑_e~n(n≥2)型Banach空间上的摄动类问题的反面回答.

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简介：TheauthorsprovetheHyers-Ulam-RassiasstabilityofthequadraticmappinginBanachmodulesoveraunitalC*-algebra,andprovetheHyers-Ulam-RassiasstabilityofthequadraticmappinginBanachmodulesoveraunitalBanachalgebra.