Stability of the Cauchy-Jensen functional equation in \(C^*\)-algebras: a fixed point approach

DOI10.1155/2008/872190zbMath1149.39025OpenAlexW1970612055WikidataQ59218468 ScholiaQ59218468MaRDI QIDQ937583

Chun-Gil Park, Jong Su An

Publication date: 15 August 2008

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/54707

zbMATH Keywords

Hyers-Ulam-Rassias stabilitygeneralized derivationsCauchy-Jensen functional equation\(C^{\ast }\)-algebra homomorphisms

Mathematics Subject Classification ID

Stability, separation, extension, and related topics for functional equations (39B82) General theory of (C^*)-algebras (46L05) Functional equations for functions with more general domains and/or ranges (39B52) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57)

Related Items (6)

Approximation of the generalized Cauchy-Jensen functional equation in \(C^\ast\)-algebras ⋮ Unnamed Item ⋮ On the stability of a functional equation deriving from additive and quadratic functions ⋮ Stability of a mixed type functional equation on multi-Banach spaces: a fixed point approach ⋮ On the stability of the generalized Cauchy-Jensen set-valued functional equations ⋮ A new coupled fixed point result in extended metric spaces with an application to study the stability of set-valued functional equations

Cites Work

• Cauchy-Rassias stability of Cauchy-Jensen additive mappings in Banach spaces
• Generalized Hyers-Ulam stability of quadratic functional equations: a fixed point approach
• Fixed point methods for the generalized stability of functional equations in a single variable
• Solution of a problem of Ulam
• On approximation of approximately linear mappings by linear mappings
• A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
• The problem of S. M. Ulam for approximately multiplicative mappings
• On the stability of functional equations in Banach spaces
• Homomorphisms between Poisson JC*-algebras
• Lie \(\ast\)-homomorphisms between Lie \(C^*\)-algebras and Lie \(\ast\)-derivations on Lie \(C^*\)-algebras
• On the stability of the linear mapping in Banach modules
• Fixed points and Hyers--Ulam--Rassias stability of Cauchy--Jensen functional equations in Banach algebras
• On the Stability of the Linear Mapping in Banach Spaces
• Hyers–Ulam–Rassias stability of a generalized Apollonius–Jensen type additive mapping and isomorphisms between C *‐algebras
• A fixed point theorem of the alternative, for contractions on a generalized complete metric space

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