Musielak－Orlicz序列空间的一些凸性

本文给出了赋Ｏｒｌｉｃｚ范数的Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ序列空间的局部一致凸性，（Ｈ）性质，（Ｓ）性质的判据．     

Musielak—Orlicz序列空间的一些凸性

本文给出了赋Ｏｒｌｉｃｚ范数的Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ序列空间的局部一致凸性，（Ｈ）性质，（Ｓ）性质的判据。     

赋Orlicz范数的Musielak-Orlicz序列空间的单调点

给出赋Ｏｒｌｉｃｚ范数的Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ序列空间中上（下）单调点以及上（下）局部一致单调点的充分必要条件．     

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．     

Orlicz序列空间的一致单调系数及应用

本文给出了Ｏｒｌｉｃｚ序列空间一致单调系数数值，同时给出了Ｏｒｌｉｃｚ序列空间具有一致单调性的条件，进而讨论具有一致单调性的Ｏｒｌｉｃｚ序列空间中的最佳逼近算子的一些特征。     

Orlicz序列空间的（弱）正规结构和（LD）性质

本文讨论赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ序列空间ＬＭ，主要结果如下：（１）ＬＭ具有Ｌａｍｉ－Ｄｏｚｏ性质     

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     

Orlicz函数空间单位球端点的一个重要特征

无论赋Ｌｕｘｅｍｂｕｒｇ范数或赋Ｏｒｌｉｃｚ范数，Ｏｒｌｉｃｚ函数空间单位球上的点为端点的充要条件是，于此点处Ｅ_Ｎ弱收敛蕴涵测度收敛．     

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．     

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．     

On the Baronti constants of Orlicz function spaces

In this paper we calculate the value of the Baronti constants of the Orlicz function spaces equipped with either the Orlicz norm or the gauge norm.     

Exact Values of Some Geometric Constants of Orlicz Spaces

We present the exact values of nonsquare constants, von Neumann-Jordan constants, Jung constants, packing constants, weakly convergent sequence coefficients and normal structure coefficients in a class of reflexive Orlicz function spaces and sequence spaces equipped with Luxemburg norm and Orlicz norm.     

Complex rotundity of Orlicz sequence spaces equipped with the p-Amemiya norm

In this paper, two equivalent definitions of complex strongly extreme points in general complex Banach spaces are shown. It is proved that for any Orlicz sequence space equipped with the p-Amemiya norm (1?p<∞, p is odd), complex strongly extreme points of the unit ball coincide with complex extreme points of the unit ball. Moreover, criteria for them in Orlicz sequence spaces equipped with the p-Amemiya norm are given. Criteria for complex mid-point locally uniform rotundity and complex rotundity of Orlicz sequence spaces equipped with the p-Amemiya norm are also deduced.     

Uniform rotundity of Orlicz function spaces equipped with the ‐Amemiya norm

Necessary and sufficient conditions for uniform rotundity of Orlicz function spaces equipped with the p‐Amemiya norm are presented. The obtained results unify, complete and widen the characterization of uniform rotundity of Orlicz spaces. In the case of the ∞‐Amemiya (i.e. the Luxemburg) norm or the 1‐Amemiya (i.e. the Orlicz) norm, these results were known earlier. Some connections with the fixed point theory and the best approximation theory are presented.     

Weak Uniform Rotundity of Orlicz Sequence Spaces

Necessary and sufficient conditions are given for weak uniform rotundity of Orlicz sequence spaces equipped with the Luxemburg norm.     

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.     

Kadec-Klee property in Musielak-Orlicz function spaces equipped with the Orlicz norm

It is well-known that the Kadec-Klee property is an important property in the geometry of Banach spaces. It is closely connected with the approximation compactness and fixed point property of non-expansive mappings. In this paper, a criterion for Musielak-Orlicz function spaces equipped with the Orlicz norm to have the Kadec-Klee property are given. As a corollary, we obtain that a class of non-reflexive Musielak-Orlicz function spaces have the Fixed Point property.

     

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.      

Maluta's coefficient in Musielak-Orlicz sequence spaces equipped with the Orlicz norm

Maluta's coefficient of Musielak-Orlicz sequence spaces equipped with the Orlicz norm is calculated. A sufficient condition for the Schur property of these spaces is given.