On the Hyers-Ulam-Rassias stability of generalized quadratic mappings in Banach modules.

DOI10.1016/J.JMAA.2003.10.027zbMath1046.39023OpenAlexW2036347655MaRDI QIDQ1426076

Chun-Gil Park

Publication date: 14 March 2004

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2003.10.027

zbMATH Keywords

stabilityBanach modulesquadratic functional equationBanach \(\ast\)-algebrageneralized \(A\)-quadratic mappings

Mathematics Subject Classification ID

Stability, separation, extension, and related topics for functional equations (39B82) Functional equations for functions with more general domains and/or ranges (39B52) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25)

Related Items (11)

On the stability of a functional equation deriving from additive and quadratic functions ⋮ The \(N\)-isometric isomorphisms in linear \(N\)-normed \(C^{\ast}\)-algebras ⋮ Fixed points and stability for quadratic mappings in \(\beta\)-normed left Banach modules on Banach algebras ⋮ The Hyers-Ulam stability of a functional equation deriving from quadratic and cubic functions in quasi-\(\beta \)-normed spaces ⋮ On the stability of a mixed functional equation deriving from additive, quadratic and cubic mappings ⋮ A new approach to Hyers-Ulam stability of \(r\)-variable quadratic functional equations ⋮ Generalized Hyers-Ulam stability of the Pexiderized Cauchy functional equation in non-archimedean spaces ⋮ On the generalized \(A\)-quadratic mappings associated with the variance of a discrete-type distribution ⋮ Ulam stability problem for generalized \(A\)-quadratic mappings ⋮ Hyers--Ulam stability of a generalized Apollonius type quadratic mapping ⋮ Asymptotic aspect of the quadratic functional equation in multi-normed spaces

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• Some results concerning the Cauchy functional equation in certain Banach algebras
• On the Stability of the Linear Functional Equation
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• On the stability of the quadratic mapping in normed spaces

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