Harmonic mappings for which second dilatation is Janowski functions - Yavuz Duman, Emel; Kahramaner, Yasemin; Darus, Maslina; POLATOĞLU, YAŞAR (My University, 2013)
In the present paper we extend the fundamental property that if h(z) and g(z) are regular functions in the open unit disc D with the properties h(0) = g(0) = 0, h maps D onto many-sheeted region which is starlike with respect to the origin, and Re g ′ (z) h′(z) > 0, then Re g(z) h(z) > 0, introduced by R.J. Libera [5] to the Janowski functions and give some applications of this to the harmonic functions.
Keywords: Harmonic mappings; Janowski functions; growth theorem; distortion theorem; coefficient inequality