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. Recently, the Hyers-Ulam-Rassias stability of the functional equation f(x + 2y) + f(x − 2y) = 2f(x) − f(2x) + 4n f(x + y) + f(x − y) o , 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