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 ( a b ) + f ( a i ( b ) ) = 2 f ( a ) f ( b ) , a , b ∈ H , where H is the Heisenberg group and the map i : H ⟶ H is an automorphism of H such that i ∘ i = i d (the identity map).