On some classes of meromorphic functions defined by subordination and superordination

Let $p\in N^*$ and $\beta,\gamma\in C$ with $\beta\neq 0$ and let $\Sigma_p$ denote the class of meromorphic functions of the form $g(z)={\ds\frac{a_{-p}}{z^p}}+a_0+a_1z+\cdots,\,z\in \dot U,\,a_{-p}\neq 0$. We consider the integral operator $J_{p,\beta,\gamma}:K_{p,\beta,\gamma}\subset\Sigma_p\to \Sigma_p$ defined by $$J_{p,\beta,\gamma}(g)(z)=\left[\frac{\gamma-p\beta}{z^\gamma }\int_0^zg^\beta(t) t^{\gamma-1}dt\right]^{\frac{1}{\beta}},\,g\in K_{p,\beta,\gamma},\,z\in \dot U.$$ We introduce some new subclasses of the class $\Sigma_p$, associated with subordination and superordination, such that, in some particular cases, these new subclasses are the well-known classes of meromorphic starlike functions and we study the properties of these subclasses with respect to the operator $J_{p,\beta,\gamma}$.