THE GENERALIZED HYERS-ULAM STABILITY OF AN ADDITIVE FUNCTIONAL EQUATION

In this article using the fixed point alternative approach, we prove the generalized Hyers-Ulam stability of the following additive functional equation f µ x + y 2 + z ¶ = f(x) + f(y) 2 + f(z): in non-Archimedean normed spaces. The concept of Hyers-Ulam-Rassias or Hyers-Ulam stability originated from the Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.