Stability of the quadratic functional equation in Lipschitz spaces

DOI10.1016/j.jmaa.2003.12.034zbMath1052.39030OpenAlexW2087972996MaRDI QIDQ1827071

Stefan Czerwik, Krzysztof Dłutek

Publication date: 6 August 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.2003.12.034

zbMATH Keywords

stabilityquadratic functional equationvector spaceAbelian groupinvariant meansLipschitz functionsLipschitz normsquadratic difference

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)

Related Items (15)

Erratum to: ``Quartic functional equations in Lipschitz spaces ⋮ Stability of functional equations in a single variable via JS-metrics ⋮ Fuzzy stability of quadratic-cubic functional equations ⋮ On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem ⋮ Behavior of bi-cubic functions in Lipschitz spaces ⋮ On fuzzy random multiobjective quadratic programming ⋮ A new type of approximation for cubic functional equations in Lipschitz spaces ⋮ Stability of generalized multi-quadratic mappings in Lipschitz spaces ⋮ Quartic functional equations in Lipschitz spaces ⋮ On approximation of approximately generalized quadratic functional equation via Lipschitz criteria ⋮ On approximate solution of Drygas functional equation according to the Lipschitz criteria ⋮ Asymptotic aspect of the quadratic functional equation in multi-normed spaces ⋮ Lipschitz stability of the k-quadratic functional equation ⋮ Almost tri-cubic functions with Lipschitz condition ⋮ Approximate solution of a generalized multi-quadratic type functional equation in Lipschitz spaces

Cites Work

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• Note on decomposition of bounded functions into the sum of periodic terms
• Lipschitz stability of the Cauchy and Jensen equations
• Stability of the Cauchy type equations in \({\mathfrak L}_ p\) norms
• Superstability of the equation of quadratic functionals in \(L^p\)-spaces
• Quadratic difference operators in \(L^p\)-spaces
• Hyers-Ulam stability of functional equations in several variables
• On some generalized invariant means and their application to the stability of the Hyers-Ulam type
• On the asymptoticity aspect of Hyers-Ulam stability of mappings
• On the Stability of the Linear Functional Equation

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