Classes of meromorphic α-convex functions

Abstract

For a fixed analytic univalent function φ, the class of meromorphic univalent α-convex functions with respect to φ 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 φ. Differential subordination and superordination conditions are also obtained for the subclass of meromorphic starlike functions with respect to φ.