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

Title & Authors
STABILITY OF (α, β, γ)-DERIVATIONS ON LIE C*-ALGEBRA ASSOCIATED TO A PEXIDERIZED QUADRATIC TYPE FUNCTIONAL EQUATION
Eghbali, Nasrin; Hazrati, Somayeh;

Abstract
In this article, we considered the stability of the following ($\small{{\alpha}}$, $\small{{\beta}}$, $\small{{\gamma}}$)-derivation $\small{{\alpha}D[x,y}$$\small{]}$$\small{={\beta}[D(x),y}$$\small{]}$$\small{+{\gamma}[x,D(y)}$$\small{]}$$\small{}$ and homomorphisms associated to the quadratic type functional equation $\small{f(kx+y)+f(kx+{\sigma}(y))=2kg(x)+2g(y),\;x,y{\in}A}$, where $\small{{\sigma}}$ is an involution of the Lie $\small{C^*}$-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
($\small{{\alpha},{\beta},{\gamma}}$)-derivation;Lie $\small{C^*}$-algebra;quadratic functional equation;
Language
English
Cited by
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