Amemiya Norm Equals Orlicz Norm in Musielak-Orlicz Spaces

Let （Ω,μ） be a a-finite measure space and Φ ： Ω × [0,∞） → [0, ∞] be a Musielak-Orlicz function. Denote by L^Φ（Ω） the Musielak-Orlicz space generated by Φ. We prove that the Amemiya norm equals the Orlicz norm in L^Φ（Ω）.     

On weak uniform normal structure in weighted Orlicz sequence spaces

It is proved that a weighted Orlicz sequence space ?M(w), equipped with Luxemburg or Amemiya norm has weak uniform normal structure iff ?M(w)≅hM(w) for wide class of weight sequences . An example is constructed, where M has not Δ₂-condition but by choosing a suitable weight sequence limn→∞wn=∞ we get that ?M(w) has weak uniform normal structure.     

Extreme Points and Strongly Extreme Points of Musielak-Orlicz Sequences Spaces

Criteria for extreme points and strongly extreme points in Musielak-Orlicz sequence spaces, equipped with both the Luxemburg norm and the Orlicz norm, are given.     

A Notion of Orlicz Spaces for Vector Valued Functions

The notion of the Orlicz space is generalized to spaces of Banach-space valued functions. A well-known generalization is based on N-functions of a real variable. We consider a more general setting based on spaces generated by convex functions defined on a Banach space. We investigate structural properties of these spaces, such as the role of the delta-growth conditions, separability, the closure of , and representations of the dual space.     

The weakly strongly exposed points of Orlicz spaces

In this paper, criteria in order that a point in an Orlicz space be a weakly strongly exposed point, or a *-weakly strongly exposed point are given, respectively. The subject supported by NSF of China.     

A note on extreme points in dual spaces

Given a normed space X it can be easily proven that every extreme point in B _X *, the unit ball of X*, is the restriction of an extreme point in B _X ***. Our purpose is to study when the restrictions of extreme points in B _X *** are extreme points in B _X *. Namely, we characterize L ₁-preduals satisfying the aforementioned property.     

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

该文给出赋0rlicz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．     

赋Orlicz范数的Orlicz—Lorentz空间的严格凸性

本文对于赋Ｌｕｘｅｍｂｕｒｇ范数的Ｏｒｌｉｃｚ－Ｌｏｒｅｎｔｚ空间     

Musielak-Orlicz序列空间的粗性

作者给出赋Luxemburg范数Musielak-Orlicz序列空间光滑点的支撑泛函的刻画．进一步,给出赋Orliez范数和赋Luxemburg范数Musielak-Orlicz序列空间的粗性,点态粗的充分必要条件．     

Musielak—Orlicz序列空间的光滑性质

本文给出了Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｅｚ序列空间简洁的光滑点判据,从而得到十分便于应用的空间光滑性判别条件,同时纠正了「１」中主要定理的错误。     

On the compactly locally uniformly rotund points of Orlicz spaces

In this paper, locally uniformly rotund points and compactly locally uniformly rotund points are introduced. Moreover, criteria for compactly locally uniformly rotund points in Orlicz spaces are given.     

A new premium calculation principle based on Orlicz norms

A multiplicative equivalent of the zero utility premium calculation principle is introduced. If the utility function happens to be a normalized Young function the new premium calculation principle is related to Orlicz norms.     

赋Orlicz范数的Musielak-Orlicz空间的光滑点与强光滑点(英)

给出赋Ｏｒｌｉｃｚ范数的Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ函数空间中光滑点、光滑性、强（很）光滑点和强（很）光滑性的充 分必要条件．     

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．     

Musielak-Orlicz序列空间中的S-点

本文给出了Musielak-Orlicz序列空间中S-点的充要判别准则.作为推论,得到Musielak-Orlicz序列空间具有S-性质的充分必要条件.     

Sequence spaces of fuzzy real numbers defined by Orlicz functions

In this article we study different properties of convergent, null and bounded sequence spaces of fuzzy real numbers defined by an Orlicz function, like completeness, solidness, symmetricity, convergence free etc. We prove some inclusion results, too. The work of the first author was carried under University Grants Commission of India project No.-F. No. 30-240/2004 (RS).     

Local rotundity structure of Cesàro-Orlicz sequence spaces

Some criteria for extreme points and strong U-points in Cesàro-Orlicz spaces are given. In consequence we find a Cesàro-Orlicz sequence space different from c₀ which has no extreme points. Some examples show that in these spaces the notion of the strong U-point is essentially stronger than the notion of the extreme point. Various examples presented in this paper show that there are some differences between criteria for extreme points and strong U-points in Orlicz spaces and in Cesàro-Orlicz spaces. We also show that the uniqueness of the local best approximation needs the notion of SU-point, that is, the notion of the extreme point is not strong enough here.     

Orlicz空间的P凸性

赋Orlicz范数的Orlicz空间的P凸等价于自反。     

Generalized difference sequence spaces on seminormed space defined by Orlicz functions

In this paper we define the sequence space ℓ _M (Δ ^m , p, q, s) on a seminormed complex linear space by using an Orlicz function. We study its different algebraic and topological properties like solidness, symmetricity, monotonicity, convergence free etc. We prove some inclusion relations involving ℓ _M (Δ ^m , p, q, s).