Properties of a Class of Meromorphic Univalent Functions

Abstract

In this paper, we study a subclass of meromorphic functions defined in the unit disk having a simple pole in it. A sufficient condition that guarantees the univalence of functions belonging to this subclass is derived. Inspired by this condition, we define a new subclass of meromorphic univalent functions in the unit disk characterized by a specific differential inequality. We derive a formula to represent functions in this subclass. Furthermore, conditions which are necessary and sufficient for membership of functions in terms of its Taylor's coefficient are obtained adjoined with a sharp estimate for the associated Fekete–Szeg"o functional.