Approximately Quadratic Mappings on Restricted Domains.

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. [ABSTRACT FROM AUTHOR]