Nonlinear L-Fuzzy stability of cubic functional equations

Abstract

We establish some stability results for the cubic functional equations (Equation) (Equation) and (Equation) in the setting of various L-fuzzy normed spaces that in turn generalize a Hyers-Ulam stability result in the framework of classical normed spaces. First, we shall prove the stability of cubic functional equations in the L-fuzzy normed space under arbitrary tnorm which generalizes previous studies. Then, we prove the stability of cubic functional equations in the non-Archimedean L-fuzzy normed space. We therefore provide a link among different disciplines: fuzzy set theory, lattice theory, non-Archimedean spaces, and mathematical analysis. © 2012 Agarwal et al.