Quasiconformal Harmonic Mappings Related to Janowski Starlike Functions

Abstract

Let f(z) = h(z) + <(g(z))over bar> be a univalent sense-preserving harmonic mapping of the open unit disc D = {z vertical bar vertical bar z vertical bar < 1}. If f satisfies the condition vertical bar omega(z)vertical bar= vertical bar g'(z)/h'(z)vertical bar< k, 0 < k < 1, then is called k-quasiconformal harmonic mapping in D. The main purpose of this paper was to give some properties of the class of k-quasiconformal mappings related to Janowski starlike functions.