K-extreme point of generalized orlicz sequence spaces with Luxemburg norm

2013 ◽  
Vol 53 (2) ◽  
Author(s):  
Zhongrui Shi
Keyword(s):  
Extreme Point ◽  
Sequence Spaces ◽  
Luxemburg Norm ◽  
Orlicz Sequence Spaces

scholarly journals The Modulus of Nearly Uniform Smoothness in Orlicz Sequence Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Shaoyong Zhang ◽  
Meiling Zhang ◽  
Yujia Zhan
Keyword(s):  
Fixed Point ◽  
Sequence Spaces ◽  
Point Property ◽  
Luxemburg Norm ◽  
Continuous Norm ◽  
Absolutely Continuous ◽  
Uniform Smoothness ◽  
Orlicz Sequence Spaces ◽  
Köthe Sequence Spaces ◽  
Equivalent Conditions

It is well known that the modulus of nearly uniform smoothness related with the fixed point property is important in Banach spaces. In this paper, we prove that the modulus of nearly uniform smoothness in Köthe sequence spaces without absolutely continuous norm is ΓX(t)=t. Meanwhile, the formula of the modulus of nearly uniform smoothness in Orlicz sequence spaces equipped with the Luxemburg norm is given. As a corollary, we get a criterion for nearly uniform smoothness of Orlicz sequence spaces equipped with the Luxemburg norm. Finally, the equivalent conditions of R(a,l(Φ))<1+a and RW(a,l(Φ))<1+a are given.

scholarly journals Smooth, very smooth and strongly smooth points in Musielak-Orlicz sequence spaces

2001 ◽  
Vol 63 (3) ◽  
pp. 441-457 ◽  
Author(s):  
Shurong Bian ◽  
Henryk Hudzik ◽  
Tingfu Wang
Keyword(s):  
Sequence Spaces ◽  
Luxemburg Norm ◽  
Orlicz Sequence Spaces

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

Weakly compact sets in Orlicz sequence spaces

2021 ◽  
pp. 1-14
Author(s):  
Siyu Shi ◽  
Zhongrui Shi ◽  
Shujun Wu
Keyword(s):  
Sequence Spaces ◽  
Compact Sets ◽  
Weakly Compact ◽  
Orlicz Sequence Spaces ◽  
Weakly Compact Sets
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