Stabilities of Cubic Mappings in Fuzzy Normed Spaces

• Main Authors: Ghaffari Ali, Alinejad Ahmad
• Format: Article
• Language: English
• Published: SpringerOpen 2010-01-01
• Series: Advances in Difference Equations
• Online Access: http://www.advancesindifferenceequations.com/content/2010/150873

<p/> <p>Rassias(2001) introduced the pioneering cubic functional equation in the history of mathematical analysis: <inline-formula><graphic file="1687-1847-2010-150873-i1.gif"/></inline-formula> 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-formula><graphic file="1687-1847-2010-150873-i2.gif"/></inline-formula> to the cubic functional equations. In this paper, we prove the Ulam-Hyers stability of the cubic functional equation: <inline-formula><graphic file="1687-1847-2010-150873-i3.gif"/></inline-formula> 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.</p>