Orlicz序列空间的对偶映射

本文研究Orlicz序列空间的对偶映射,给出对偶映象集为弱紧集的充分必要 条件.作为推论,得到Orlicz序列空间的弱接近光滑性的充要条件.     

Orlicz序列空间的强暴露点

本文给出赋Orlicz范数和赋Luxemburg范数的Orlicz序列空间的单位球面上的强暴露点的充分必要条件．     

关于Orlicz序列空间的包含关系

设Φ,Ψ为一对互余的Ｎ－函数,本文给出了包含关系成立的充要条件,并修正Ｃｈｅｎ［１,ｐ,１６８］的一个例子.     

On Decomposition in Exponential Orlicz Spaces

Various characterizations are given of the exponential Orlicz space L and the Orlicz‐Lorentz space L. By way of application we give a simple proof of the celebrated theorem of Brézis and Wainger concerning a limiting case of a Sobolev imbedding theorem.     

The U—property of Orlicz Sequence Spaces

LetXbeaBanachspace,X'bethedualofX,S(X)={xeX:IIxII=l},B(X)={x6X:llxIlS1}betheunitsphereandunitballofX,respectively.ForxeX,let7xdenotethesetofsupportingfunctionalsfofS(X.)atx.Inl978,LauKa-singintroducedthefollowingnotiontostudytheChebyshevsubsetofX[1j:DefinitionABanachspaceXissaidtohaveU-propertyifforanyE>O,thereexists3>osuchthatSomeoftheresultsofU-propertyin[ljaresummarizedinthefollowing.Theorem(I)IfXhasU-property,thenXisuniformlynonSquare,inparticular,Xissuper-reflexive(infactr…     

赋Orlicz范数的Orlicz序列空间的接近一致凸性

本文给出了赋Ｏｒｌｉｃｚ序列空间的Ｈ点的充分必要条件,进而得至了赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ序列空间具有（Ｈ）性质的判据．同时给出了赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ序列空间的一致ＵＫＫ和接近一致凸性的等价条件。     

The Lyapunov Theorem for Measures Valued in Orlicz Sequence Spaces

It is proved that the closure of the range of a nonatomic countably additive measure with values in an Orlicz space l _M, where 2 [_M,_M], is convex.     

赋Orlicz范数的Orlicz空间中最佳逼近算子

在赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ空间中,给出最佳逼近算子单调性的一个充分条件和最佳逼近元存在定理．     

Orlicz空间中支撑映射的上(下)半连续点

该文给出了赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ空间Ｌ°Ｍ中的点是支撑映射的上（下）半连续点的充分必要条件;推出了支撑映射为上（下）半连续的判别准则．     

Orlicz序列空间的粗系数

证明了Orlicz序列空间lm的粗系数R（lm）=2／supky,这里‖y‖0n=1ky=min{k＞0：‖y‖0n=1/k（1＋PN（ky））}．     

Maluta＇s Coefficient of Musielak-Orlicz Sequence Spaces

In this paper, we give the formula of Maluta＇s coefficient for calculation, and don＇t add any conditions to the generating function Ф.     

赋Orlicz范数下Orlicz-Lorentz序列空间的一致正规结构和一致非方性

Orlicz-Lorent空间作为经典Orlicz空间的推广,为调和分析及微分方程提供了合理的空间框架,而一致正规结构和一致非方性在不动点理论领域有着重要的应用.本文给出了赋Orlicz范数下Orlicz-Lorentz序列空间具有一致正规结构和一致非方性的充要条件.     

Orlicz空间上支撑映射的半连续性

给出赋Luxemburg范数的Orlicz空间上支撑映射上（下）半连续的判别准则。     

On Some Applications of Geometry of Banach Spaces and Some New Results Related to the Fixed Point Theory in Orlicz Sequence Spaces

We present some applications of the geometry of Banach spaces in the approximation theory and in the theory of generalized inverses. We also give some new results, on Orlicz sequence spaces, related to the fixed point theory. After a short introduction, in Section 2 we consider the best approximation projection from a Banach space $X$ onto its non-empty subset and proximinality of the subspaces of order continuous elements in various classes of Köthe spaces. We present formulas for the distance to these subspaces of the elements from the outside of them. In Section 3 we recall some results and definitions concerning generalized inverses of operators (metric generalized inverses and Moore-Penrose generalized inverses). We also recall some results on the perturbation analysis of generalized inverses in Banach spaces. The last part of this section concerns generalized inverses of multivalued linear operators (their definitions and representations). The last section starts with a formula for modulus of nearly uniform smoothness of Orlicz sequence spaces $\ell^\Phi$equipped with the Amemiya-Orlicz norm. From this result a criterion for nearly uniform smoothness of these spaces is deduced. A formula for the Domínguez-Benavides coefficient $R(a,l_\Phi)$ is also presented, whence a sufficient condition for the weak fixed point property of the space $\ell^\Phi$is obtained.     

On a Class of Generalized Lacunary Difference Sequence Spaces Defined by Orlicz Functions

In this article we introduce the generalized lacunary difference sequence spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and [N_θ,M,Δ~m]_∞using m~(th)- difference.We study their properties like completeness,solidness,symmetricity.Also we obtain some inclusion relations involving the spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and[N_θ,M,Δ~m]_∞and the Cesàro summable and strongly Cesàro summable sequences.     

Approximative Properties of Diagonal Operators in Orlicz Spaces

We obtain the exact values of some important approximative quantities (such as the best approximation, the basis width, Kolmogorov's width, and the best n-term approximation) of certain sets of images of the diagonal operators in the Orlicz sequence spaces l _M .     

赋Orlicz范数的Musielak Orlicz序列空间的Gateaux可微点

该文给出赋Orlicz 范数的Musielak Orlicz序列空间中Gateaux可微点（光滑点）与Frechet可微点（强光滑点）的判定准则.在此基础上推出了该空间具有光滑性或强光滑性的充分必要条件.      

弱紧集与Orlicz空间

本文圆满完善了[1]的结果,并由此给出了Ｏｒｌｉｃｚ空间自反性与Ｓｈｕｒ定理的新证明。     

WCS Coefficients in Orlicz Sequence Spaces

We introduce some practical calculation of the weakly convergent sequence coefficients of Orlicz sequence spaces equipped with Luxemburg norm and Orlicz norm. For the N-function (u) of which the index function is monotonuous, the exact value WCS(l⁽⁾) of Orlicz sequence space l⁽⁾ with Luxemburg norm is available, i.e. WCS(l⁽⁾) = or WCS(l) of l with Orlicz norm has the exact value or estimation