Approximate Homomorphisms of Ternary Semigroups

Abstract

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.

arXiv comment10 pages

References in corpus (7)

• On Foundation of the Generalized Nambu Mechanics
• Hypersymmetry: a Z_3-graded generalization of supersymmetry
• The cubic chessboard
• Universal differential calculus on ternary algebras
• On the Orthogonal Stability of the Pexiderized Quadratic Equation
• On the Stability of J*-Homomorphisms
• Approximately Vanishing of Topological Cohomology Groups

Cited by in corpus (1)

• On the ternary complex analysis and its applications