On the stability of approximately additive mappings. (English) Zbl 0961.47039

Lee, Yang-Hi; Jun, Kil-Woung

Proc. Am. Math. Soc. 128, No. 5, 1361-1369 (2000).

The authors prove generalizations of results by Hyers, Ulam and Rassias on existence and uniqueness of a subadditive mapping \(T:G \to X\), where \(G\) is a vector space and \(X\) is a Banach space, which approximates in a suitable sense a given map \(f:G\to X\) satisfying a condition such as \(\|f(x+y)-f(x)-f(y) \|\leq \phi(x,y)\) for all \(x,y \in G\) where \(\phi\) is a given map satisfying appropriate conditions.

Reviewer: J.V.A.Goncalves (Brasilia)

MSC:

47J05

Equations involving nonlinear operators (general)

Keywords:

stability; approximation; subadditive mappings