Random Stability of an Additive-Quadratic-Quartic Functional Equation

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-quartic functional equation f(x + 2y) + f (x - 2y) = 2f (x + y) + 2f (-x - y) + 2f (x - y) + 2f(y - x) - 4f(-x) - 2f(x) + f (2y) + f(-2y) - 4f(y) - 4f(-y) in complete random normed spaces.The authors would like to thank referees for giving useful suggestions for the improvement of this paper. The first author is supported by Islamic Azad University-Ayatollah Amoli Branch, Amol, Iran. The second author was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-313-C00050) and the third author was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2009-0070788). The fourth author is supported by Universita a degli Studi di Palermo, R.S. ex 60%