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

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.