Nonlinear L-fuzzy stability of k-cubic functional equation

Abstract

In this paper, we establish the stability result for the k-cubic functional equation 2[k f(x + ky) + f(kx - y)] = k(k 2 + 1)[f(x + y) + f(x - y)] + 2(k 4 - 1)f(y), where k is a real number different from 0 and 1, 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 k-cubic functional equations in the L-fuzzy normed space under arbitrary t-norm which generalizes previous works. Then we prove the stability of k-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.