Approximate Homomorphisms of Ternary Semigroups
Abstract
A mapping f:(G1,[ ]1) (G2,[ ]2) between ternary semigroups will be called a ternary homomorphism if f([xyz]1)=[f(x)f(y)f(z)]2. In this paper, we prove the generalized Hyers--Ulam--Rassias stability of mappings of commutative semigroups into Banach spaces. In addition, we establish the superstability of ternary homomorphisms into Banach algebras endowed with multiplicative norms.
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