On a subclass of harmonic mappings

Abstract

In the present paper we extent 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(z) maps D onto λ-spiral region and Ren e iλ g 0 (z) h0(z) o > 0, then Ren e iλ g(z) h(z) o > 0, and then give some applications of this to the harmonic functions.