Stability of a mixed type cubic and quartic functional equation in non-Archimedean \(\ell\)-fuzzy normed spaces. (English) Zbl 1262.39041
Summary: We prove the generalized Hyers-Ulam-Rassias stability of the mixed type cubic and quartic functional equation
\[
f(x+2y)+f(x-2y) = 4(f(x+y)+f(x-y))-24f(y)-6f(x)+3f(2y)
\]
in non-Archimedean \(\ell\)-fuzzy normed spaces.
MSC:
| 39B82 | Stability, separation, extension, and related topics for functional equations |
| 39B52 | Functional equations for functions with more general domains and/or ranges |
| 46S10 | Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis |
| 46S40 | Fuzzy functional analysis |
