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

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 Je...