On nonlinear stability in various random normed spaces

Abstract In this article, we prove the nonlinear stability of the quartic functional equation 1 6 f ( x + 4 y ) + f ( 4 x - y ) = 3 0 6 9 f x + y 3 + f ( x + 2 y ) (1) + 1 3 6 f ( x - y ) - 1 3 9 4 f ( x + y ) + 4 2 5 f ( y ) - 1 5 3 0 f ( x ) (2) (3)  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.