Celik, Shalla and Olgun defined neutro-homomorphisms in neutrosophic extended triplet groups and Zhang et al. investigated neutro-homomorphisms in neutrosophic extended triplet groups. In this note, we apply the results on neutro-homomorphisms in neutrosophic extended triplet groups to investigate C*-algebra homomorphisms in unital C*-algebras. Assume that A is a unital C*-algebra with multiplication operation ★, unit e and unitary group U(A) and that B is a unital C*-algebra with multiplication operation ★ and unitary group U(B).

Definition 1. Let (U(A), ★) and (U(B), ★) be unitary groups of unital C*-algebras A and B, respectively. A mapping h: U(A) →U(B) is called a neutro-*-homomorphism if h(u★v) = h(u)★h(v), h(u*) =  h(u)* for all u,v in U(A).

We obtain the following main result.

Theorem 1. Let A and B be unital C*-algebras. Let H: A →B be a complex-linear mapping and let h: (U(A), ★) →(U(B), ★) be a neutro-*-homomorphism. If H|_U(A) = h, then H : A→B is a C*-algebra homomorphism.

Further, we introduce and solve bi-additive functional inequalities and prove the Hyers-Ulam stability of the bi-additive functional inequalities in complex Banach spaces. This is applied to investigate b-derivations on C*-algebras, Lie C*-algebras and JC*-algebras, and derivations on C*-algebras, Lie C*-algebras and JC*-algebras associated with the bi-additive functional inequalities. Moreover, we study biderivations on C*-ternary algebras and C*-triple systems associated with the bi-additive functional inequalities.