Higher Homomorphisms and ‎Their Approximations

In this paper, we introduce a class of higher homomorphisms on an algebra 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 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.