On the existence of \(m\)-norms in vector spaces over valued fields

DOI10.1007/s00010-023-00956-zOpenAlexW4366769814MaRDI QIDQ6185262

Jens Schwaiger

Publication date: 8 January 2024

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-023-00956-z

zbMATH Keywords

normed spacetopological vector spaces\(m\)-norm

Mathematics Subject Classification ID

Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Functional inequalities, including subadditivity, convexity, etc. (39B62) Other ``topological linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than (mathbb{R}), etc.) (46A19)

Cites Work

• Unnamed Item
• On \(n\)-normed spaces
• A fixed point theorem in \(n\)-Banach spaces and Ulam stability
• On Ulam stability of a functional equation
• On a functional equation by Baak, Boo and Rassias
• n-Inner Product Spaces
• ON APPROXIMATELY ADDITIVE MAPPINGS IN 2-BANACH SPACES
• Untersuchungen über verallgemeinerte m‐metrische Räume. I

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