On Classes of Analytic Multivalent Functions Involving by Generalization of Differential Operator with Negative Coefficients

Abstract

    Let Ą( ) be the class of analytic and p-valent functions with negative coefficients .Also let     denote the subclasses of Ą( ) consisting of p-valent analytic functions with negative coefficients in the open unit disk . The object of the present paper is to prove   distortion theorems of functions in the classes   ,coefficient estimates , extreme points, closure theorems, and inclusion properties. Also, we obtain radii of convexity, starlikeness and close-to-convexity for functions belonging to those classes. By specializing the parameters involved, the corresponding results for several interesting subclasses of analytic functions can easily be deduced.