Janowski subclasses of starlike mappings

Abstract

"In this paper, two subclasses of biholomorphic starlike mappings named Janowski starlike and Janowski almost starlike with complex parameters are introduced and studied. We determine $M$ such that holomorphic mappings $f$ which satisfy the condition $\|Df(z)-I\|\le M$, $z\in B^n$, are Janowski starlike, respectively Janowski almost starlike. We also derive sufficient conditions for normalized holomorphic mappings (expressed in terms of their coefficient bounds) to belong to one of the subclasses of mappings mentioned above."