Local stability of the additive functional equation and its applications. (English) Zbl 1017.39009

Jung, Soon-Mo; Kim, Byungbae

Int. J. Math. Math. Sci. 2003, No. 1, 15-26 (2003).

The Hyers-Ulam stability of the additive functional equation for a large class of unbounded domains in Banach space is proved. Loosely speaking, it is proved that if a mapping \(f\) satisfies the additivity property approximately then there exists unique approximating additive mapping for \(f\). The result is applied to investigation of the stability of Jensen’s functional equation.

Reviewer: Claudi Alsina (Barcelona)

MSC:

39B82	Stability, separation, extension, and related topics for functional equations
39B52	Functional equations for functions with more general domains and/or ranges
39B55	Orthogonal additivity and other conditional functional equations

Keywords:

local stability; additive functional equation; Hyers-Ulam stability; Banach space; additive mapping; Jensen’s functional equation