Approximately Lie ternary (σ,τ,ξ)-derivations on Banach ternary algebras

2009/03/04 by M. Eshaghi Gordji, Gordji, M. Eshaghi, R. Farrokhzad +3
Mathematics · #17A40 #39B52 #46B99 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:17A40 #msc:39B52 #msc:46B99

paper · pdf · doi:10.48550/arxiv.0903.0834

8 pages

arxiv created 2009/10/08 · arxiv updated 2009/12/01

Abstract

Let A be a Banach ternary algebra over a scalar field \Bbb R or \Bbb C and X be a ternary Banach A-module. Let σ,τ and ξ be linear mappings on A, a linear mapping D:(A,[]_A)→ (X,[]_X) is called a Lie ternary (σ,τ,ξ)-derivation, if D([abc]_A)=[[D(a)bc]_X]_(σ,τ,ξ)+[[D(b)ac]_X]_(σ,τ,ξ)+[[D(c)ba]_X]_(σ,τ,ξ), for all a,b,c∈ A, where [abc]_(σ,τ,ξ)=aτ(b)ξ(c)-σ(c)τ(b)a. In this paper, we investigate the generalized Hyers--Ulam--Rassias stability of Lie ternary (σ,τ,ξ)-derivations on Banach ternary algebras.

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