Starlike function of complex order. (English) Zbl 0596.30017

Nasr, M. A.; Aouf, M. K.

J. Nat. Sci. Math. 25, No. 1, 1-12 (1985).

The authors consider the class of normalized analytic functions f satisfying \[ Re\{1+b^{-1}(zf'(z)/f(z)-1)\}>0 \] inside the unit disc for a nonzero complex number b. Using the properties of functions with positive real part in the unit disc several properties of the above mentioned class are investigated.

Reviewer: V.Karunakaran

MSC:

30C45

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

Keywords:

functions with positive real part