Fuzzy stability of quintic functional equations: a fixed point approach

Abstract

In \cite{mmm, mm08}, the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated.

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following quintic functional equations \begin{eqnarray*} && f(3x+y) -5 f(2x+y) + f(2x-y) + 10f(x+y) - 5f(x-y) \\ && \quad = 10 f(y) + f(3x) -3 f(2x) -27 f(x) , \nonumber \\ && f(3x+y) -5 f(2x+y) + f(2x-y) + 10f(x+y) - 5f(x-y) \\ && \quad = 10 f(y) - 5f(3x) +42 f(2x) -9 f(x) \nonumber \end{eqnarray*} in fuzzy Banach spaces.