The Modulus of Nearly Uniform Smoothness in Orlicz Sequence Spaces
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...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/8674091 |
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| author | Shaoyong Zhang Meiling Zhang Yujia Zhan |
| author_facet | Shaoyong Zhang Meiling Zhang Yujia Zhan |
| author_sort | Shaoyong Zhang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d8c92e9c7c9b4e688df3bbac38d0f011 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-d8c92e9c7c9b4e688df3bbac38d0f0112025-02-03T01:10:09ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/86740918674091The Modulus of Nearly Uniform Smoothness in Orlicz Sequence SpacesShaoyong Zhang0Meiling Zhang1Yujia Zhan2Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, ChinaDepartment of Mathematics, Harbin University of Science and Technology, Harbin 150080, ChinaDepartment of Mathematics, Harbin University of Science and Technology, Harbin 150080, ChinaIt 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.http://dx.doi.org/10.1155/2019/8674091 |
| spellingShingle | Shaoyong Zhang Meiling Zhang Yujia Zhan The Modulus of Nearly Uniform Smoothness in Orlicz Sequence Spaces Journal of Function Spaces |
| title | The Modulus of Nearly Uniform Smoothness in Orlicz Sequence Spaces |
| title_full | The Modulus of Nearly Uniform Smoothness in Orlicz Sequence Spaces |
| title_fullStr | The Modulus of Nearly Uniform Smoothness in Orlicz Sequence Spaces |
| title_full_unstemmed | The Modulus of Nearly Uniform Smoothness in Orlicz Sequence Spaces |
| title_short | The Modulus of Nearly Uniform Smoothness in Orlicz Sequence Spaces |
| title_sort | modulus of nearly uniform smoothness in orlicz sequence spaces |
| url | http://dx.doi.org/10.1155/2019/8674091 |
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