A fixed-point approach to the stability of a functional equation on quadratic forms

Abstract

Abstract Using the fixed-point method, we prove the generalized Hyers-Ulam stability of the functional equation f ( x + y , z + w ) + f ( x - y , z - w ) = 2 f ( x , z ) + 2 f ( y , w ) . The quadratic form f : ℝ × ℝ → ℝ given by f(x, y) = ax2 + bxy + cy2 is a solution of the above functional equation.

Keywords

• alternative of fixed point
• functional equation
• quadratic form
• stability