由准模块生成的准规范空间

IF 1.5 3区数学 Q1 MATHEMATICS

Journal of Inequalities and Applications Pub Date : 2024-06-28 DOI:10.1186/s13660-024-03162-w

Paweł Foralewski, Henryk Hudzik, Paweł Kolwicz

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引用次数: 0

摘要

在本文中，我们引入了准模态的概念，并证明了单位准模态球的相应闵科夫斯基函数成为准规范。这样，我们参考并完成了与模数和凸模数概念相关的著名理论，这两个概念分别导致了 F 准则和规范。我们利用得到的结果来考虑准规范的卡尔德隆-洛扎诺夫斯基空间 $E_{varphi}$ 的基本性质，其中下马图谢夫斯基-奥利奇指数 $alpha _{varphi}$ 起着关键作用。我们的研究尽可能全面。

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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-norm and to the norm, respectively. We use the obtained results to consider the basic properties of quasinormed Calderón–Lozanovskiĭ spaces $E_{\varphi}$ , where the lower Matuszewska–Orlicz index $\alpha _{\varphi}$ plays the key role. Our studies are conducted in a full possible generality.

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来源期刊

Journal of Inequalities and Applications 数学-数学

自引率

6.20%

发文量

136

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.