On nonlinear stability in various random normed spaces

Abstract

In this article, we prove the nonlinear stability of the quartic functional equation 16f (x + 4y) + f (4x - y) =306 [ 9f ( x + y /3 ) + f (x + 2y) ] + 136f (x - y) - 1394f (x + y) + 425f (y) - 1530f (x) in the setting of random normed spaces Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean space, the theory of fixed point theory, the theory of intuitionistic spaces and the theory of functional equations are also presented in the article. © 2011 Rassias et al.