Suppose that is a linear space, a fuzzy normed space, a fuzzy Banach space, , a fixed integer.
The authors consider the stability of the functional equation
The main result reads, roughly, as follows. Suppose that satisfy and
for all , where is a control mapping satisfying , with some .
Then, there exists a unique quadratic function and a unique additive function such that the mapping approximates (in terms of the fuzzy norm ).
Moreover, if is odd, it can be approximated by an additive function and if is even, a quadratic mapping approximates .