Approximate Homomorphisms of Ternary Semigroups

Details Approximate Homomorphisms of Ternary Semigroups Approximate Homomorphisms of Ternary Semigroups

2005-11-10

arxiv.org/abs/math-ph/0511039v1

Lett. Math. Phys. 77 (2006), 1-9.

Physics

Mathematical Physics

10 pages

Scientific paper

10.1007/s11005-005-0042-6

A mapping $f:(G_1,[ ]_1)\to (G_2,[ ]_2)$ 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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