A functional equation having monomials as solutions

摘要

For each n=1,2,3, we obtain the general solution and the stability of the functional equationf(2x+y)+f(2x-y)=2n-2[f(x+y)+f(x-y)+6f(x)].And we obtain the general solution and the stability of the functional equationf(2x+y)+f(2x-y)+6f(y)=4[f(x+y)+f(x-y)+6f(x)].Using the fixed point method, we prove the generalized Hyers–Ulam stability of these functional equations.