Summary: We define the generalized Roper-Suffridge extension operator \(\Phi_{n,\beta_2,\gamma_2,\dots,\beta_n,\gamma_n}(f)\) on Reinhardt domain \(D_p\) as
\[ \Phi_{n,\beta_2,\gamma_2,\dots,\beta_n,\gamma_n}(f)(z)=\left(f(z_1),\left(\frac{f(z_1)}{z_1}\right)^{\beta_2}\left(f'(z_1)\right)^{\gamma_2}z_2,\dots,\left(\frac{f(z_1)}{z_1}\right)^{\beta_n}\left(f'(z_1)\right)^{\gamma_n} z_n\right) \]
for \(z=(z_1,z_2,\dots,z_n)\in D_p\), where \(D_p= \{(z_1, z_2,\dots, z_n)\in\mathbb C^n : \sum^n_{j=1} |z_j|^{p_j}< 1\}\), \(p = (p_1, p_2,\dots, p_n)\), \(p_j>0\), \(0\leq\gamma_j\leq 1-\gamma_j\), \(0\leq \beta_j\leq 1\), \(j=1,2,\dots,n\), and we choose the branch of the power functions such that \((\frac{f(z_1)}{z_1})^{\beta_j} |_{z_1=0} = 1\) and \((f'(z_1))^{\gamma_j} |_{z_1=0} = 1\), \(j=2,\dots,n\).
We show that the operator \(\Phi_{n,\beta_2,\gamma_2,\dots,\beta_n,\gamma_n}(f)\) preserves almost spirallike mappings of type \(\beta\) and order \(\alpha\) and spirallike mappings of type \(\beta\) and order \(\alpha\) on \(D_p\) for some suitable constants \(\beta_j, \gamma_j, p_j\). The results improve corresponding results of earlier authors.