Generalized Hyers–Ulam stability for general additive functional equations in quasi- β-normed spaces

• Published in: Journal of mathematical analysis and applications Vol. 356; no. 1; pp. 302 - 309
• Main Authors: Rassias, John Michael, Kim, Hark-Mahn
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.08.2009; Elsevier
• Subjects: ( [formula omitted])-Banach spaces; Contractively subadditive; Difference and functional equations, recurrence relations; Exact sciences and technology; Expansively superadditive; Finite differences and functional equations; Functional analysis; Generalized Hyers–Ulam stability; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Quasi- β-normed spaces; Sciences and techniques of general use; Contractively subadditive; Expansively superadditive; ( β , p )-Banach spaces; Quasi- β-normed spaces; Generalized Hyers–Ulam stability; Functional; Generalized Hyers-Ulam stability; (β, p)-Banach spaces; Mathematical analysis; Functional equation; Banach space; Quasi-β-normed spaces; Application; Numerical stability
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2009.03.005

In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. The first author of this paper investigated the Hyers–Ulam stability of Cauchy and Jensen type additive mappings. In this paper we generalize results obtained for Jensen type mappings and establish new theorems about the Hyers–Ulam stability for general additive functional equations in quasi- β-normed spaces.