Solution and stability of a quadratic functional equation in Banach space and its application (Q2911957)

The authors prove the generalized Hyers-Ulam-Rassias stability of the quadratic type functional equation \(f\left(\frac{x_0+x_1}{2}\right)+f\left(\frac{x_0-x_1}{2}\right)+f\left(\frac{x_2+x_3}{2}\right)+f\left(\frac{x_2-x_3}{2}\right) =\frac{1}{2}(f(x_0)+f(x_1)+f(x_2)+f(x_3))\) in Banach spaces by using the usual direct method.