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On a problem of G. Isac and Th. M. Rassias concerning the stability of mappings. (English) Zbl 0993.47002
Let $\psi: \bbfR_+\to \bbfR_+$ be a mapping. Let $E_1$, $E_2$ be normed spaces. A mapping $f: E_1\to E_2$ is said to be $\psi$-additive if there is a $\theta> 0$ such that $$\|f(x+ y)- f(x)- f(y)\|\le\theta(\psi\|x\|+\psi\|y\|)$$ for all $x,y\in E_1$. There are given: an answer to a problem of G. Isac and Th. M. Rassias concerning Hyers-Ulam-Rassias stability of linear mappings and a new characterization of $\psi$-additive mappings.

47A05General theory of linear operators
47A30Operator norms and inequalities
Full Text: DOI
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