On the stability of a cubic functional equation in random normed spaces

Abstract. The concept of Hyers-Ulam-Rassias stability has been originated from a stability theorem due to Th. M. Rassias. Re-cently, the Hyers-Ulam-Rassias stability of the functional equation f(x+ 2y) + f(x − 2y) = 2f(x) − f(2x) + 4 f(x+ y) + f(x − y) has been proved in the case of Banach spaces. In this paper, we will find out the generalized Hyers-Ulam-Rassias stability problem of the above functional equation in random normed spaces. AMS Subject Classification: 39B72; 47H09