Copyright © 2010 Ali Ghaffari and Ahmad Alinejad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Rassias (2001) introduced the pioneering cubic functional equation in the history of mathematical analysis: f(x+2y)−3f(x+y)+3f(x)−f(x−y)=6f(y) and solved the pertinent famous Ulam stability problem for this inspiring equation. This Rassias cubic functional equation was the historic transition from the following famous Euler-Lagrange-Rassias quadratic functional equation: f(x+y)−2f(x)+f(x−y)=2f(y) to the cubic functional equations. In this paper, we prove the Ulam-Hyers stability of the cubic functional equation: f(x+3y)−3f(x+y)+3f(y−x)−f(x−3y)=48f(y) in fuzzy normed linear spaces. We use the definition of fuzzy normed linear spaces to establish a fuzzy version of a generalized Hyers-Ulam-Rassias stability for above equation in the fuzzy normed linear space setting. The fuzzy sequentially continuity of the cubic mappings is discussed.