Ulam stability of a quartic functional equation

Abstract

The oldest quartic functional equation was introduced by J. M. Rassias in (1999), and then was employed by other authors. The functional equation f (2 x + y) + f (2 x - y) = 4 f (x + y) + 4 f (x - y) + 24 f (x) - 6 f (y) is called a quartic functional equation, all of its solution is said to be a quartic function. In the current paper, the Hyers-Ulam stability and the superstability for quartic functional equations are established by using the fixed-point alternative theorem. © 2012 Abasalt Bodaghi et al.