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On the Hyers-Ulam stability of \(\psi\)-additive mappings. (English) Zbl 0770.41018
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.

MSC:
41A30 Approximation by other special function classes
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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