A unital $C^*$ -- algebra $mathcal A,$ endowed with the Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie $C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and $g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A $Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is called a Lie $(g,h)$ -- double derivation if $f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all $a,b in mathcal A.$ In this paper, our main purpose is to prove the generalized Hyers –- Ulam –- Rassias stability of Lie $*$ - double derivations on Lie $C^*$ - algebras associated with the following additive mapping: begin{align*} sum^{n}_{k=2}(sum^{k}_{i_{1}=2} sum^{k+1}_{i_{2}=i_{1}+1}... sum^{n}_{i_{n-k+1}=i_{n-k}+1}) f( sum^{n}_{i=1, ineq i_{1},..,i_{n-k+1} } x_{i}&-sum^{n-k+1}_{ r=1}x_{i_{r}})+f(sum^{n}_{ i=1} x_{i}) \&=2^{n-1} f(x_{1}) end{align*} for a fixed positive integer $n$ with $n geq 2.$
Ghobadipour, N. (2010). Lie $^*$-double derivations on Lie $C^*$-algebras. International Journal of Nonlinear Analysis and Applications, 1(2), 63-71. doi: 10.22075/ijnaa.2010.76
MLA
N. Ghobadipour. "Lie $^*$-double derivations on Lie $C^*$-algebras". International Journal of Nonlinear Analysis and Applications, 1, 2, 2010, 63-71. doi: 10.22075/ijnaa.2010.76
HARVARD
Ghobadipour, N. (2010). 'Lie $^*$-double derivations on Lie $C^*$-algebras', International Journal of Nonlinear Analysis and Applications, 1(2), pp. 63-71. doi: 10.22075/ijnaa.2010.76
VANCOUVER
Ghobadipour, N. Lie $^*$-double derivations on Lie $C^*$-algebras. International Journal of Nonlinear Analysis and Applications, 2010; 1(2): 63-71. doi: 10.22075/ijnaa.2010.76
)