Stability of a pexiderial functional equation in random normed spaces

Abstract

The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72:297-300, 1978. Recently, the generalized Hyers-Ulam-Rassias stability of the following quadratic functional equation f(x+y)+f(x-y)=2f(x)+2f(y) proved in the earlier work. In this paper, using direct method we prove the generalized Hyers-Ulam stability of the following Pexiderial functional equation f(x+y)+f(x-y)=2g(x)+2g(y) in random normed space. © 2011 Springer-Verlag.