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http://dx.doi.org/10.4134/CKMS.2016.31.1.101

STABILITY OF (α, β, γ)-DERIVATIONS ON LIE C^*-ALGEBRA ASSOCIATED TO A PEXIDERIZED QUADRATIC TYPE FUNCTIONAL EQUATION

Eghbali, Nasrin (Department of Mathematics Faculty of Mathematical Sciences University of Mohaghegh Ardabili)
Hazrati, Somayeh (Department of Mathematics Faculty of Mathematical Sciences University of Mohaghegh Ardabili)

Publication Information

Communications of the Korean Mathematical Society / v.31, no.1, 2016 , pp. 101-113 More about this Journal

Abstract

In this article, we considered the stability of the following ( ${\alpha}$ , ${\beta}$ , ${\gamma}$ )-derivation $$${\alpha}D[x,y$ $]$ $={\beta}[D(x),y$ $]$ $+{\gamma}[x,D(y)$ $]$ $$$$ and homomorphisms associated to the quadratic type functional equation $f(kx+y)+f(kx+{\sigma}(y))=2kg(x)+2g(y),\;x,y{\in}A$ , where ${\sigma}$ is an involution of the Lie $C^*$ -algebra A and k is a fixed positive integer. The Hyers-Ulam stability on unbounded domains is also studied. Applications of the results for the asymptotic behavior of the generalized quadratic functional equation are provided.

Keywords

( ${\alpha},{\beta},{\gamma}$ )-derivation; Lie $C^*$ -algebra; quadratic functional equation;

Citations & Related Records

Reference

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KSCI

STABILITY OF (α, β, γ)-DERIVATIONS ON LIE C*-ALGEBRA ASSOCIATED TO A PEXIDERIZED QUADRATIC TYPE FUNCTIONAL EQUATION

STABILITY OF (α, β, γ)-DERIVATIONS ON LIE C^*-ALGEBRA ASSOCIATED TO A PEXIDERIZED QUADRATIC TYPE FUNCTIONAL EQUATION