Quasinormed spaces generated by a quasimodular

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 -n...

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Published inJournal of inequalities and applications Vol. 2024; no. 1; pp. 86 - 18
Main Authors Foralewski, Paweł, Hudzik, Henryk, Kolwicz, Paweł
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 28.06.2024
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Mathematics
Mathematics and Statistics
Quasimodular
Quasinormed Calderón–Lozanovskiĭ space
Quasinormed ideal space
Quasinormed ideal space
46A80
46A16
Quasinormed Calderón–Lozanovskiĭ space
Quasimodular
46E30
46B20
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Summary: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 E φ , where the lower Matuszewska–Orlicz index α φ plays the key role. Our studies are conducted in a full possible generality.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-024-03162-w