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- Title
Monotonicities in Orlicz Spaces Equipped with Mazur-Orlicz F-Norm.
- Authors
Bai, Xinran; Cui, Yunan; Kończak, Joanna
- Abstract
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.
- Subjects
SEQUENCE spaces; CONVEX functions; GENERATING functions; ORLICZ spaces
- Publication
Journal of Function Spaces, 2020, p1
- ISSN
2314-8896
- Publication type
Article
- DOI
10.1155/2020/8512636