Mathematica Eterna
Open Access

Abstract

Harmonic Mappings for which Second Dilatation is Janowski Functions

Emel Yavuz Duman, Ya¸sar Polato˘glu, Yasemin Kahramaner and Maslina Darus

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. 618 Emel Yavuz Duman,Ya¸sar Polato˘glu,Yasemin Kahramaner and Maslina Darus