On subclasses for generalized operators of complex order. (English) Zbl 1168.30304

Darus, Maslina; Ibrahim, Rabha W.

Far East J. Math. Sci. (FJMS) 33, No. 3, 299-308 (2009).

From the authors’ abstract: We define generalized differential and integral operators on the class of analytic functions in the unit disk involving the \(k\)-th Hadamard product. These operators are generalizations of some well-known operators, for example, the Sălăgean operator and the Al-Oboudi operator. New classes containing these operators of complex order are investigated.

MSC:

30C45

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

Keywords:

Hadamard product; integral operator; differential operator; Sălăgean operator; Al-Oboudi operator