On a Cauchy-Jensen functional equation and its stability

DOI10.1016/J.JMAA.2005.09.028zbMath1104.39027OpenAlexW1973293998MaRDI QIDQ852778

Jae-Hyeong Bae, Won-Gil Park

Publication date: 15 November 2006

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.2005.09.028

zbMATH Keywords

Hyers-Ulam-Rassias stabilitysystem of functional equationsCauchy-Jensen mapping

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) Systems of functional equations and inequalities (39B72)

Related Items (17)

On a Jensen-cubic functional equation and its Hyers-Ulam stability ⋮ On Hyers-Ulam stability of two functional equations in non-Archimedean spaces ⋮ Generalized stability of classical polynomial functional equation of order \(n\) ⋮ Generalized Ulam-Hyers stability of \(C^*\)-ternary algebra \(n\)-homomorphisms for a functional equation ⋮ Unnamed Item ⋮ Stability of a 2-dimensional functional equation in a class of vector variable functions ⋮ A fixed point approach to the stability of a Cauchy-Jensen functional equation ⋮ Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stabilities of an additive functional equation in several variables ⋮ On the generalized Hyers-Ulam stability of a Cauchy-Jensen functional equation ⋮ Stability of a Cauchy-Jensen functional equation in quasi-Banach spaces ⋮ Hyers-Ulam stability of a bi-Jensen functional equation on a punctured domain ⋮ On the asymptoticity aspect of Hyers-Ulam stability of quadratic mappings ⋮ On a functional equation connected with bi-linear mappings and its Hyers-Ulam stability ⋮ Stability of a bi-additive functional equation in Banach modules over a \(C^\star\)-algebra ⋮ On stability and hyperstability of an equation characterizing multi-Cauchy-Jensen mappings ⋮ On stability of a general bilinear functional equation ⋮ Remarks on the Hyers-Ulam stability of some systems of functional equations

Cites Work

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• On the Hyers-Ulam stability of the functional equations that have the quadratic property
• A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
• Quadratic functional equation and inner product spaces
• On the Stability of the Linear Mapping in Banach Spaces
• On the Stability of the Linear Functional Equation
• On the stability of the quadratic mapping in normed spaces

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