About an integral operator preserving meromorphic starlike functions (Q1280213)

Let \(\Sigma_k\), \(k\geq 0\), denote the class of meromorphic functions of the form \(f(z)= {1\over z}+ a_kz^k+ \dots\), in the unit disk \(s=\{z: | z|<1\}\), \(f\) being regular in \(0<| z|<1\). Let \(\Sigma_k^*\) denote the class of starlike functions \(g\) of the form \(g(z)=z+ a_{n+1}z^{n+1} + \cdots, z\in s\), \(n\geq 1\), the author shows that the integral operator \(Lg,c,\nu :\Sigma_0\to \Sigma_0\) defined by \(Lg,c,\nu (f)(z)={c \over g^{c+1}(z)} \int^z_0 f(t)g^c(t)e^{\nu tp[}dt\), \(z\in D\), \(f\in\Sigma_0\), maps \(\Sigma_k^*\) to \(\Sigma_\ell^*\) where \(\ell=\min \{p-1,k\}\). The author also has given an example which preserves meromorphically starlike functions.