Hyers-Ulam-Rassias stability of the additive-quadratic mappings in non-Archimedean Banach spaces

Abstract

Using the fixed point and direct methods, we prove the generalized Hyers-Ulam stability of the following additive-quadratic functional equation in non-Archimedean normed spaces r[f(x + y + z/s) + f(x - y + z/s) + f(x + y - z/s) + f(-x + y + z/s)] = gamma f(x) + gamma f(y) + gamma f(z), where r, s, gamma are positive real numbers.