Approximately Quadratic Mappings on Restricted Domains

Abstract

In this paper, we introduce a generalized quadratic functional equation $f(rx+sy)=rf(x)+sf(y)-rsf(x-y)$ where $r,s$ are nonzero real numbers with $r+s=1.$ We show that this functional equation is quadratic if $r,s$ are rational numbers. We also investigate its stability problem on restricted domains. These results are applied to study of an asymptotic behavior of these generalized quadratic mappings.

9 pages