Stabilities of Cubic Mappings in Fuzzy Normed Spaces

Rassias(2001) introduced the pioneering cubic functional equation in the history of mathematical analysis: [inline-graphic not available: see fulltext] 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: [inline-graphic not available: see fulltext] to the cubic functional equations. In this paper, we prove the Ulam-Hyers stability of the cubic functional equation: [inline-graphic not available: see fulltext] 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.