A fixed point approach to the Hyers-Ulam stability of an AQ functional equation on \({\beta}\)-Banach modules

DOI10.1186/1029-242X-2012-204zbMath1277.39046WikidataQ59288154 ScholiaQ59288154MaRDI QIDQ386779

Tian Xu, John Michael S. Rassias

Publication date: 10 December 2013

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

zbMATH Keywords

Hyers-Ulam stabilityfixed point method\(\beta\)-Banach moduleadditive and quadratic equation

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) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25)

Cites Work

• Hyers-Ulam stability of zeros of polynomials
• On approximately additive functions
• Generalized Hyers-Ulam stability for a general mixed functional equation in quasi-\(\beta \)-normed spaces
• On stability of additive mappings
• A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
• Stability of functional equations in single variable.
• Hyers-Ulam stability of functional equations in several variables
• Fixed points and stability for quadratic mappings in \(\beta\)-normed left Banach modules on Banach algebras
• Proprieta’ locali e approssimazione di operatori
• A fixed point theorem of the alternative, for contractions on a generalized complete metric space
• On the Stability of the Linear Functional Equation
• Remarks on the stability of functional equations
• Approximate homomorphisms
• On the stability of the quadratic mapping in normed spaces

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