On the Hyers-Ulam Stability of the Functional Equations That Have the Quadratic Property

Abstract

The Hyers-Ulam stability of the quadratic functional equation (1) on a restricted domain shall be investigated, and the result shall be applied to the study of an asymptotic behavior of that equation. Furthermore, the Hyers-Ulam stability problems of another quadratic equation (4) (on a restricted domain) shall also be treated under the approximately even (or odd) condition, and some asymptotic behaviors of the quadratic mappings and the additive mappings shall be investigated. © 1998 Academic Press.