Lineare 2-normierte Räume†

n-Inner Product Spaces†

Given an n-normed space with n ≥ 2, we offer a simple way to derive an (n−1)- norm from the n-norm and realize that any n-normed space is an (n − 1)-normed space. We also show that, in certain cases, the (n − 1)-norm can be derived from the n-norm in such a way that the convergence and completeness in the n-norm is equivalent to those in the derived (n − 1)-norm. Using this fact, we prove a fixed point theorem for some n-Banach spaces.

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ON n-NORMED SPACES

2‐Banach Spaces

We study the space lp, 1 ≤ p ≤ ∞, and its natural n-norm, which can viewed as a generalisation of its usual norm. Using a derived norm equivalent to its usual norm, we show that lp is complete with respect to its natural n-norm. In addition, we also prove a fixed point theorem for lp as an n-normed space.

/pdf/the-space-of-p-summable-sequences-and-its-natural-n-norm-lo6s08vjzn.pdf

The space of p -summable sequences and its natural n -norm

Untersuchungen über verallgemeinerte m‐metrische Räume. II

Geometric Integration Theory

L'integrale de Lebesgue-Stieltjes Ensembles et operations mesurables $(B)$ dans les espaces metriques Groupes Espaces vectoriels generaux Espaces du type $(F)$ Espaces normes Espaces du type $(B)$ Operations totalement continues et associees Suites biorthogonales Fonctionnelles lineaires dans les espaces du type $(B)$ Suites faiblement convergentes d'elements Equations fonctionnelles lineaires Isometrie, equivalence, isomorphie Dimension lineaire Convergence faible dans les espaces du type $(B)$ Remarques Note. Sur la mesure de Haar Auteurs Cites Index Terminologique.

Lineare 2-normierte Räume†

Citations

n-Inner Product Spaces†

ON n-NORMED SPACES

2‐Banach Spaces

The space of p -summable sequences and its natural n -norm

Untersuchungen über verallgemeinerte m‐metrische Räume. II

References

Geometric Integration Theory

Théorie des opérations linéaires

2-metrische Räume und ihre topologische Struktur†‡‡

Area and normality.

Zum Inhaltsbegriff in der Minkowskischen Geometrie

Related Papers (5)

ON n-NORMED SPACES

n-Inner Product Spaces†

2-metrische Räume und ihre topologische Struktur†‡‡

On the Stability of the Linear Functional Equation

Sur la convergence statistique