scholarly journals Strongly Extreme Points in Orlicz Function Spaces

1995 ◽  
Vol 189 (3) ◽  
pp. 651-670 ◽  
Author(s):  
H. Hudzik ◽  
W. Kurc ◽  
M. Wisla
Keyword(s):  
Orlicz Function ◽  
Extreme Points ◽  
Function Spaces

scholarly journals Extreme Points and Rotundity in Musielak-Orlicz-Bochner Function Spaces Endowed with Orlicz Norm

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Shaoqiang Shang ◽  
Yunan Cui ◽  
Yongqiang Fu
Keyword(s):  
Extreme Point ◽  
Orlicz Function ◽  
Extreme Points ◽  
Function Spaces ◽  
Orlicz Norm

The criteria for extreme point and rotundity of Musielak-Orlicz-Bochner function spaces equipped with Orlicz norm are given. Although criteria for extreme point of Musielak-Orlicz function spaces equipped with the Orlicz norm were known, we can easily deduce them from our main results.

Criteria for complex strongly extreme points of Musielak–Orlicz function spaces

2009 ◽  
Vol 70 (6) ◽  
pp. 2270-2276 ◽  
Author(s):  
Lili Chen ◽  
Yunan Cui ◽  
Henryk Hudzik
Keyword(s):  
Orlicz Function ◽  
Extreme Points ◽  
Function Spaces

scholarly journals Complex Convexity of Musielak-Orlicz Function Spaces Equipped with thep-Amemiya Norm

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Lili Chen ◽  
Yunan Cui ◽  
Yanfeng Zhao
Keyword(s):  
Unit Ball ◽  
Function Space ◽  
Orlicz Function ◽  
Extreme Points ◽  
Function Spaces ◽  
Strict Convexity ◽  
Uniform Convexity ◽  
Amemiya Norm

The complex convexity of Musielak-Orlicz function spaces equipped with thep-Amemiya norm is mainly discussed. It is obtained that, for any Musielak-Orlicz function space equipped with thep-Amemiya norm when1≤p<∞, complex strongly extreme points of the unit ball coincide with complex extreme points of the unit ball. Moreover, criteria for them in above spaces are given. Criteria for complex strict convexity and complex midpoint locally uniform convexity of above spaces are also deduced.

Orlicz Spaces Without Strongly Extreme Points and Without H-Points

1993 ◽  
Vol 36 (2) ◽  
pp. 173-177 ◽  
Author(s):  
Henryk Hudzik
Keyword(s):  
Extreme Point ◽  
Orlicz Space ◽  
Unit Sphere ◽  
Orlicz Function ◽  
Orlicz Spaces ◽  
Extreme Points ◽  
Luxemburg Norm ◽  
Nonatomic Measure

AbstractW. Kurc [5] has proved that in the unit sphere of Orlicz space LΦ(μ) generated by an Orlicz function Φ satisfying the suitable Δ2-condition and equipped with the Luxemburg norm every extreme point is strongly extreme. In this paper it is proved in the case of a nonatomic measure μ that the unit sphere of the Orlicz space LΦ(μ) generated by an Orlicz function Φ which does not satisfy the suitable Δ2-condition and equipped with the Luxemburg norm has no strongly extreme point and no H-point.

scholarly journals Strongly Extreme Points and Middle Point Locally Uniformly Convex in Orlicz Spaces Equipped with s-Norm

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Yunan Cui ◽  
Yujia Zhan
Keyword(s):  
Banach Spaces ◽  
Orlicz Space ◽  
Necessary Conditions ◽  
Orlicz Function ◽  
Orlicz Spaces ◽  
Extreme Points ◽  
Uniformly Convex ◽  
Middle Point ◽  
Sufficient And Necessary Conditions

As is well known, the extreme points and strongly extreme points play important roles in Banach spaces. In this paper, the criterion for strongly extreme points in Orlicz spaces equipped with s-norm is given. We complete solved criterion-Orlicz space that generated by Orlicz function. And the sufficient and necessary conditions for middle point locally uniformly convex in Orlicz spaces equipped with s-norm are obtained.

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