The superstability of d’Alembert’s functional equation on the Heisenberg group

In this paper, we investigate the superstability of d’Alembert’s functional equation f(ab)+f(ai(b))=2f(a)f(b),a,b∈H, where HH is the Heisenberg group and the map i:H⟶Hi:H⟶H is an automorphism of HH such that i∘i=idi∘i=id (the identity map).