On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations

摘要

We achieve the general solution and the generalized Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stabilities for quadratic functional equationsf(ax+by)+f(ax−by)=(b(a+b)/2)f(x+y)+(b(a+b)/2)f(x−y)+(2a2−ab−b2)f(x)+(b2−ab)f(y)wherea, bare nonzero fixed integers withb≠±a,−3a, andf(ax+by)+f(ax−by)=2a2f(x)+2b2f(y)for fixed integersa, bwitha,b≠0anda±b≠0.