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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/8512636 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 2314-8896 2314-8888 |