Quasinormed spaces generated by a quasimodular
[ 1 ] Instytut Matematyki, Wydział Automatyki, Robotyki i Elektrotechniki, Politechnika Poznańska | [ P ] employee
2024
scientific article
english
- quasimodular
- quasinormed ideal space
- quasinormed Calderón–Lozanovskiĭ space
EN In this paper, we introduce the notion of a quasimodular and we prove that the respective Minkowski functional of the unit quasimodular ball becomes a quasinorm. In this way, we refer to and complete the well-known theory related to the notions of a modular and a convex modular that lead to the F-norm and to the norm, respectively. We use the obtained results to consider the basic properties of quasinormed Calderón–Lozanovskiĭ spaces Eϕ, where the lower Matuszewska–Orlicz index αϕ plays the key role. Our studies are conducted in a full possible generality.
86-1 - 86-18
https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-024-03162-w
Article number: 86
CC BY (attribution alone)
open journal
final published version
at the time of publication
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