On a certain subclass of analytic functions involving differential operators. (English) Zbl 1243.30009

Abubaker, Afaf; Darus, Maslina

Transylv. J. Math. Mech. 3, No. 1, 1-8 (2011).

Summary: We introduce a new subclass of normalized analytic functions in the open unit disc which is defined by a certain differential operator. A coefficient inequality, distortion theorems and extreme points of differential operator for this class are given. We also discuss the boundedness properties associated with partial sums of functions in the class \(TS^{\sigma,s}_{\lambda,\delta}(\beta,\gamma,n)\).

MSC:

30C45

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Keywords:

analytic functions; coefficient inequalities; partial sums; starlike functions