A note on the definition of a generalized fuzzy normed space

We reconsider the definition of a generalized fuzzy normed space from [I. Goleţ, On generalized fuzzy normed spaces and coincidence point theorems, Fuzzy Sets and Systems 161 (2010) 1138–1144], showing that the mapping used in the homogeneity axiom must satisfy the multiplicative Cauchy functional equation. Therefore, generalized fuzzy normed spaces are, in fact, fuzzy p  -normed spaces with p>0p>0.