Hyperstability of Some Functional Equations on Restricted Domain

Abstract

The paper concerns functions which approximately satisfy, not necessarily on the whole linear space, a generalization of linear functional equation. A Hyers-Ulam stability result is proved and next applied to give conditions implying the hyperstability of the equation. The results may be used as tools in stability studies on restricted domains for various functional equations. We use the main theorem to obtain a few hyperstability results of Fréchet equation on restricted domain for different control functions.