The stability of a cubic type functional equation with the fixed point alternative

In this note we investigate the generalized Hyers–Ulam–Rassias stability for the new cubic type functional equation f (x +y +2z)+f (x +y −2z)+f (2x)+f (2y) = 2[f (x +y)+2f (x +z)+ 2f (x − z) + 2f (y + z) + 2f (y − z)] by using the fixed point alternative. The first systematic study of fixed point theorems in nonlinear analysis is due to G. Isac and Th.M. Rassias [Internat. J. Math. Math. Sci. 19 (1996) 219–228].  2004 Elsevier Inc. All rights reserved.