Cauchy-Rassias stability of Cauchy-Jensen additive mappings in Banach spaces

DOI10.1007/s10114-005-0697-zzbMath1118.39012OpenAlexW2119403583MaRDI QIDQ882748

Chun-Gil Park

Publication date: 24 May 2007

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-005-0697-z

zbMATH Keywords

Hyers-Ulam-Rassias stabilityBanach algebrafunctional equationsisomorphismCauchy additive mappingJensen additive 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)

Related Items (28)

Stability of Cauchy-Jensen Type Functional Equation in (2, α)–Banach Spaces ⋮ Approximation of the generalized Cauchy-Jensen functional equation in \(C^\ast\)-algebras ⋮ Unnamed Item ⋮ Hyperstability of Cauchy-Jensen functional equations ⋮ Isometric isomorphisms in proper \(CQ^*\)-algebras ⋮ On the Hyers–Ulam stability and hyperstability of a generalized quadratic functional equation in n-Banach spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Isomorphisms between \(C^{*}\)-ternary algebras ⋮ The hyperstability of AQ-Jensen functional equation on 2-divisible abelian group and inner product spaces ⋮ Unnamed Item ⋮ On the hyperstability of a quartic functional equation in Banach spaces ⋮ ISOMORPHISMS,DERIVATIONS AND ISOMETRIES IN PROPER <i>CQ</i>^&#8727;-ALGEBRAS ⋮ Unnamed Item ⋮ Non-Archimedean hyperstability of a Cauchy-Jensen type functional equation ⋮ Stability of Cauchy-Jensen type functional equation in generalized fuzzy normed spaces ⋮ Stability of the Cauchy-Jensen functional equation in \(C^*\)-algebras: a fixed point approach ⋮ On Hyers-Ulam-Rassias stability of functional equations ⋮ Stability of functional equations in several variables ⋮ Isomorphisms and derivations in Lie \(C^{\ast}\)-algebras ⋮ Fixed points and Hyers--Ulam--Rassias stability of Cauchy--Jensen functional equations in Banach algebras ⋮ Approximately linear mappings in Banach modules over a \(C^*\)-algebra ⋮ On the stability of a cubic functional equation ⋮ Non-Archimedean hyperstability of Cauchy-Jensen functional equations on a restricted domain ⋮ On the stability of the generalized Cauchy-Jensen set-valued functional equations ⋮ Jordan *-derivations on \(C^*\)-algebras and \(JC^*\)-algebras ⋮ On the hyperstability of a Cauchy-Jensen type functional equation in Banach spaces ⋮ STABILITY OF THE JENSEN TYPE FUNCTIONAL EQUATION IN BANACH ALGEBRAS: A FIXED POINT APPROACH

Cites Work

• Unnamed Item
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• On approximation of approximately linear mappings by linear mappings
• On a modified Hyers-Ulam sequence
• Variational problem of some quadratic functionals in complex analysis
• A generalization of the Hyers-Ulam-Rassias stability of Jensen's equation
• A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
• Hyers--Ulam--Rassias stability of quadratic functional equations in Banach modules over a \(C^{\ast}\)-algebra
• The problem of S. M. Ulam for approximately multiplicative mappings
• On the stability of functional equations and a problem of Ulam
• On the stability of functional equations in Banach spaces
• On the stability of the linear mapping in Banach modules
• On the Hyers-Ulam stability of linear mappings
• Homomorphisms between \(JC^*\)-algebras and Lie \(C^*\)-algebras
• Universal Jensen's equations in Banach modules over a \(C^*\)-algebra and its unitary group
• New Generalizations of Jensen's Functional Equation
• On the Behavior of Mappings which do not Satisfy Hyers-Ulam Stability
• On the Stability of the Linear Mapping in Banach Spaces
• HOMOMORPHISMS BETWEEN C*-ALGEBRAS ASSOCIATED WITH THE TRIF FUNCTIONAL EQUATION AND LINEAR DERIVATIONS ON C*-ALGEBRAS
• On the Stability of the Linear Functional Equation

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