Fuzzy Stability in the Sense of Hyers-Ulam of a Functional Equation on Quadratic Forms

Abstract

We obtain a general solution of the 2-variable quadratic functional equation zeta(y(1) + y(2), y(3) + y(4)) + zeta(y(1)-y(2), y(3)-y(4)) = 2 zeta(y(1), y(3)) + 2 zeta(y(2), y(4)) and discuss the stability of the above functional equation, while the quadratic form zeta(a, b) = alpha a(2) + beta ab + gamma c(2) is a solution of our functional equation.