Stability of Additive Functional Equation on Discrete Quantum Semigroups

Abstract. 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.