Higher Homomorphisms and ‎Their Approximations

‎In this paper‎, ‎we introduce a class of higher homomorphisms on an algebra $ \mathcal{A} $ and we characterize the structure of them as a linear combination of some ‎sequences‎ of homomorphisms‎.‎ ‎Also ‎‎we prove that for any approximate higher ring homomorphism on a Banach algebra $ \mathcal{A} $ under some sequences of control funtions‎, there exists a unique higher ring homomorphism near it. Using special sequences of control functions, we show that the approximate higher ring homomorphism is an exact higher ring homomorphism.