Perturbation of generalized derivations in fuzzy Menger normed algebras

In this paper we introduce a notion for fuzzy Menger normed algebra. Then we will investigate continuity of algebraic operations in this space. We will show that the class of all fuzzy Menger normed algebras strictly contains the class of normed algebras. Finally, we will prove Hyers–Ulam–Rassias superstability of generalized derivation functional equation f ( ax + by + vw ) = af ( x ) + bf ( y ) + vf ( w ) + g ( v ) w ( x , y , v , w ∈ X ; 0 ≠ a , b ∈ C ) in complete fuzzy Menger normed algebras. A few applications of our results will be exhibited.