Starlike function of complex order. (English) Zbl 0596.30017

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


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