Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2015.05.27
  • Published : 2016.01.31
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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.

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References

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