STABILITY PROBLEMS DERIVING FROM MIXED ADDITIVE AND QUADRATIC FUNCTIONAL EQUATIONS

Let n >= 2 be an integer. We obtain the solution of the following mixed additive and quadratic functional equation (4 - n)r(t) f(Sigma(n)(j=1) x(j)/r) + Sigma(n)(i=1)f (Sigma(n)(j=1) (-1)(delta ij) x(j)/r) = 2(t)Sigma(n)(i=1) f(x(i)), where t is an element of {1, 2}, r is an element of R (r not equal n/2, 2 and r(2) not equal n) and the function delta is a Kronecker delta, and we prove the stability in normed group by using shadowing property and the Hyers-Ulam-Rassias stability in Banach spaces.