Isac, George; Rassias, Themistocles M. On the Hyers-Ulam stability of \(\psi\)-additive mappings. (English) Zbl 0770.41018 J. Approximation Theory 72, No. 2, 131-137 (1993). Summary: Let \(E_ 1\) be a real normed vector space and \(E_ 2\) a real Banach space. S. M. Ulam posed the problem: When does a linear mapping near an approximately additive mapping \(f: E_ 1\to E_ 2\) exist? We give a new generalization solution to Ulam’s problem for \(\psi\)-additive mappings. Some relations with the asymptotic differentiability are also indicated. Cited in 2 ReviewsCited in 99 Documents MSC: 41A30 Approximation by other special function classes 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) Keywords:Ulam’s problem; asymptotic differentiability PDFBibTeX XMLCite \textit{G. Isac} and \textit{T. M. Rassias}, J. Approx. Theory 72, No. 2, 131--137 (1993; Zbl 0770.41018) Full Text: DOI