On approximate n-Jordan homomorphisms
Abstract
The aim of this paper it to characterize n-Jordan homomorphisms and to investigate their connection with n-homomorphisms as well as homomorphisms. Furthermore, the following implication is also verified: if a function ϕ is additive and (for a fixed integer n≥2) the mapping x ↦ ϕ(xn)-ϕ(x)n satisfies some mild regularity assumption, then the function ϕ is an n-homomorphism or it is a continuous additive function.
Keywords
homomorphism; Jordan homomorphism; n-(Jordan) homomorphism; polynomial function
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Institute of Mathematics, University of Debrecen, Hungary Hungary
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