On a certain family of univalent functions with negative coefficients defined by the Ruscheweyh derivative

Abstract

By making use of the Ruscheweyh derivative we introduce and study a certain family of univalent functions with negative coefficients which are regular in the unit disc U = ${z :mid zmid< I}$. In this paper we have obtained sharp results including coefficient estimates, closure theorems and modified Hadamard products of several functions belonging to this class. We also obtain radii of close - to - convexity, starlikeness and convexity for functions belonging to this class and consider an integral operator associated with functions belonging to this class.