Monotonicities in Orlicz Spaces Equipped with Mazur-Orlicz F-Norm
Some basic properties in Orlicz spaces and Orlicz sequence spaces that are generated by monotone function equipped with the Mazur-Orlicz F-norm are studied in this paper. We give some relationships between the modulus and the Mazur-Orlicz F-norm. We obtain an interesting result that the norm of an e...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/8512636 |
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| author | Xinran Bai Yunan Cui Joanna Kończak |
| author_facet | Xinran Bai Yunan Cui Joanna Kończak |
| author_sort | Xinran Bai |
| collection | DOAJ |
| description | Some basic properties in Orlicz spaces and Orlicz sequence spaces that are generated by monotone function equipped with the Mazur-Orlicz F-norm are studied in this paper. We give some relationships between the modulus and the Mazur-Orlicz F-norm. We obtain an interesting result that the norm of an element in line segments is formed by two elements on the unit sphere less than or equal to 1 if and only if that the monotone function is a convex function. The criterion that Orlicz spaces and Orlicz sequence spaces that are generated by monotone function equipped with the Mazur-Orlicz F-norm are strictly monotone or lower locally uniform monotone is presented. |
| format | Article |
| id | doaj-art-63afc81ed80c40aab2986c4eb391b0e7 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-63afc81ed80c40aab2986c4eb391b0e72025-08-20T03:34:29ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/85126368512636Monotonicities in Orlicz Spaces Equipped with Mazur-Orlicz F-NormXinran Bai0Yunan Cui1Joanna Kończak2Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, ChinaDepartment of Mathematics, Harbin University of Science and Technology, Harbin 150080, ChinaFaculty of Mathematics and Computer Science, Adam Mickiewicz University in Poznań, ul. Umultowska 87, 61-614 Poznań, PolandSome basic properties in Orlicz spaces and Orlicz sequence spaces that are generated by monotone function equipped with the Mazur-Orlicz F-norm are studied in this paper. We give some relationships between the modulus and the Mazur-Orlicz F-norm. We obtain an interesting result that the norm of an element in line segments is formed by two elements on the unit sphere less than or equal to 1 if and only if that the monotone function is a convex function. The criterion that Orlicz spaces and Orlicz sequence spaces that are generated by monotone function equipped with the Mazur-Orlicz F-norm are strictly monotone or lower locally uniform monotone is presented.http://dx.doi.org/10.1155/2020/8512636 |
| spellingShingle | Xinran Bai Yunan Cui Joanna Kończak Monotonicities in Orlicz Spaces Equipped with Mazur-Orlicz F-Norm Journal of Function Spaces |
| title | Monotonicities in Orlicz Spaces Equipped with Mazur-Orlicz F-Norm |
| title_full | Monotonicities in Orlicz Spaces Equipped with Mazur-Orlicz F-Norm |
| title_fullStr | Monotonicities in Orlicz Spaces Equipped with Mazur-Orlicz F-Norm |
| title_full_unstemmed | Monotonicities in Orlicz Spaces Equipped with Mazur-Orlicz F-Norm |
| title_short | Monotonicities in Orlicz Spaces Equipped with Mazur-Orlicz F-Norm |
| title_sort | monotonicities in orlicz spaces equipped with mazur orlicz f norm |
| url | http://dx.doi.org/10.1155/2020/8512636 |
| work_keys_str_mv | AT xinranbai monotonicitiesinorliczspacesequippedwithmazurorliczfnorm AT yunancui monotonicitiesinorliczspacesequippedwithmazurorliczfnorm AT joannakonczak monotonicitiesinorliczspacesequippedwithmazurorliczfnorm |