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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)
##### Keywords:
Ulam’s problem; asymptotic differentiability
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