Fixed points and the random stability of a mixed type cubic, quadratic and additive functional equation

Abstract

Mihet and Radu, investigated the random Stability problems for the Cauchy functional equation and the Jensen functional equation via fixed point method. In this paper, we prove the Hyers-Ulam stability of a mixed type cubic, quadratic and additive functional equation f (x + ky) + f (x - ky) = k(2)f (x + y) + k(2)f (x - y) + 2(1 - k(2))f(x) for a fixed integer k with k not equal +/- 1 in random normed spaces via fixed point method.