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.

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.

scholarly journals Complex Convexity of Orlicz Modular Sequence Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Lili Chen ◽  
Deyun Chen ◽  
Yang Jiang
Keyword(s):  
Sequence Space ◽  
Extreme Points ◽  
Strict Convexity ◽  
Sequence Spaces ◽  
Uniform Convexity ◽  
Uniformly Convex ◽  
Strictly Convex ◽  
Modular Spaces

The concepts of complex extreme points, complex strongly extreme points, complex strict convexity, and complex midpoint locally uniform convexity in general modular spaces are introduced. Then we prove that, for any Orlicz modular sequence spacelΦ,ρ,lΦ,ρis complex midpoint locally uniformly convex. As a corollary,lΦ,ρis also complex strictly convex.

scholarly journals P-Convexity Property in Musielak-Orlicz Function Space of Bohner Type

2017 ◽  
Vol 3 (1) ◽  
pp. 221
Author(s):  
Yulia Romadiastri
Keyword(s):  
Banach Space ◽  
Function Space ◽  
Orlicz Function ◽  
Function Spaces ◽  
Convexity Property

<div style="text-align: justify;">In this paper, we described about Musielak-Orlicz function spaces of Bochner type. It has been obtained that Musielak-Orlicz function space <a href="https://www.codecogs.com/eqnedit.php?latex=L_\phi(\mu,X)" target="_blank"><img title="L_\phi(\mu,X)" src="https://latex.codecogs.com/gif.latex?L_\phi(\mu,X)" alt="" /></a> of Bochner type becomes a Banach space. It is described also about P-convexity of Musielak-Orlicz function space <a href="https://www.codecogs.com/eqnedit.php?latex=\small&amp;space;L_\phi(\mu,X)" target="_blank"><img title="\small L_\phi(\mu,X)" src="https://latex.codecogs.com/gif.latex?\small&amp;space;L_\phi(\mu,X)" alt="" /></a> of Bochner type. It is proved that the Musielak-Orlicz function space <a href="https://www.codecogs.com/eqnedit.php?latex=\small&amp;space;L_\phi(\mu,X)" target="_blank"><img title="\small L_\phi(\mu,X)" src="https://latex.codecogs.com/gif.latex?\small&amp;space;L_\phi(\mu,X)" alt="" /></a> of Bochner type is P-convex if and only if both spaces <a href="https://www.codecogs.com/eqnedit.php?latex=\small&amp;space;L_\phi" target="_blank"><img title="\small L_\phi" src="https://latex.codecogs.com/gif.latex?\small&amp;space;L_\phi" alt="" /></a> and X are P-convex.©2017 JNSMR UIN Walisongo. All rights reserved.</div>

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

Almost transitivity of some function spaces

1994 ◽  
Vol 116 (3) ◽  
pp. 475-488 ◽  
Author(s):  
Peter Greim ◽  
James E. Jamison ◽  
Anna Kamińska
Keyword(s):  
Unit Ball ◽  
Orlicz Space ◽  
Orlicz Spaces ◽  
Extreme Points ◽  
Function Spaces ◽  
Separable Spaces

AbstractThe almost transitive norm problem is studied for Lp (μ, X), C(K, X) and for certain Orlicz and Musielak-Orlicz spaces. For example if p ≠ 2 < ∞ then Lp (μ) has almost transitive norm if and only if the measure μ is homogeneous. It is shown that the only Musielak-Orlicz space with almost transitive norm is the Lp-space. Furthermore, an Orlicz space has an almost transitive norm if and only if the norm is maximal. Lp (μ, X) has almost transitive norm if Lp(μ) and X have. Separable spaces with non-trivial Lp-structure fail to have transitive norms. Spaces with nontrivial centralizers and extreme points in the unit ball also fail to have almost transitive norms.

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
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