On new class of analytic functions defined by using differintegral operator. (English) Zbl 1359.30029

Salman, Jumana Hekma; Joudah, Ahmed Sallal

Int. J. Adv. Appl. Math. Mech. 2, No. 1, 92-99 (2014).

Summary: Making use a fractional differintegral operator. We introduce a new class of univalent analytic functions in the unit disk \(U\). Among the results investigated for this class of functions include the coefficient inequalities, starlikenees, convexity, close-to-convexity, extreme points and Integral means inequalities.

MSC:

30C45	Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50	Coefficient problems for univalent and multivalent functions of one complex variable

Keywords:

fractional calculus (fractional integral and fractional derivative); univalent functions; principle of subordination