Generalized Hyers-Ulam stability for general additive functional equations in quasi-\(\beta \)-normed spaces

DOI10.1016/j.jmaa.2009.03.005zbMath1168.39015OpenAlexW2016808667MaRDI QIDQ1023025

Hark-Mahn Kim, John Michael S. Rassias

Publication date: 10 June 2009

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.2009.03.005

zbMATH Keywords

functional equationgeneralized Hyers-Ulam stabilitycontractively subadditiveexpansively superadditive(\(\beta.p)\)-Banach spacesquasi-\(\beta\) normed spaces

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 (39)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Refined Hyers--Ulam approximation of approximately Jensen type mappings
• Solution of a problem of Ulam
• On stability of additive mappings
• On a conjecture of Z. Ditzian
• A generalization of the Hyers-Ulam-Rassias stability of Jensen's equation
• A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
• On the Ulam stability of Jensen and Jensen type mappings on restricted domains
• Stability of homomorphisms for a 3D Cauchy-Jensen type functional equation on \(C^{*}\)-ternary algebras
• Asymptotic behavior of alternative Jensen and Jensen type functional equations
• On the stability of the linear transformation in Banach spaces
• On Riemann integration of functions with values in topological linear spaces
• On the Behavior of Mappings which do not Satisfy Hyers-Ulam Stability
• Stability of Isometries
• On the Stability of the Linear Mapping in Banach Spaces
• Stability of the Cauchy functional equation in quasi-Banach spaces
• Classes of transformations and bordering transformations
• On the Stability of the Linear Functional Equation

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