CLASSES OF MEROMORPHIC α-CONVEX FUNCTIONS

Abstract

For a fixed analytic univalent function $\phi$, the class of meromorphic univalent $\alpha$-convex functions with respect to $\phi$ is introduced. A representation theorem for functions in the class, as well as a necessary and sufficient condition for functions to belong to the class are obtained. Also we obtain a sharp growth theorem and estimate on a certain coefficient functional for meromorphic starlike functions with respect to $\phi$. Differential subordination and superordination conditions are also obtained for the subclass of meromorphic starlike functions with respect to $\phi$.