On a Certain Subclass of Analytic Functions Involving the Al-Oboudi Differential Operator

摘要

In this paper we introduce a new subclass of normalized analytic functions in the open unit disc which is defined by the Al-Oboudi differential operator. A coefficient inequality, extreme points and integral mean inequalities of a differential operator for this class are given. We investigate various subordination results for the subclass of analytic functions and obtain sufficient conditions for univalent close-to-starlikeness. We also discuss the boundedness properties associated with partial sums of functions in the class. Several interesting connections with the class of close-to-starlike and close-to-convex functions are also pointed out.