Homomorphisms and derivations in induced fuzzy C*-algebras

Using fixed point method, we establish the Hyers-Ulam stability of the fuzzy $^*-$homomorphisms in fuzzy $C^*$-algebras and fuzzy $^*$-derivations on fuzzy $C^*$-algebras associated to the following $(m,n)$-Cauchy-Jensen additive functional equation $$\sum_{\begin{subarray}{c}1\leq i_1<\cdots