On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces

Recently, the stability of the cubic functional equation f (2x + y) + f(2x - y) = 2f (x + y) + 2f (x - y) + 12f (x) in fuzzy normed spaces was proved in earlier work; and the stability of the additive functional equations f(x + y) = f(x) + f(y), 2f((x + y)/2) = f(x) + f(y) in random normed spaces was proved as well. In this paper, we prove the stability of the cubic functional equation f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 12f(x) in random normed spaces by an alternative proof which provides a better estimation. Finally, we prove the stability of the quartic functional equation f(2x + y) + f(2x - y) = 4f(x + y) + 24f(x) - 6f(y) in random normed spaces. Copyright (C) 2008 E. Baktash et al.