Stability of additive functional equation on discrete quantum semigroups

We construct a non-commutative analog of additive functional equations on discrete quantum semigroups and show that this non-commutative functional equation has Hyers-Ulam stabil- ity on amenable discrete quantum semigroups. The discrete quan- tum semigroups that we consider in this paper, are in the sense of van Daele, and the amenability is in the sense of B edos-Murphy- Tuset. Our main result generalizes a famous and old result due to Forti on the Hyers-Ulam stability of additive functional equations on amenable classical discrete semigroups