Mathematica Eterna
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Abstract

Some Results on a Subclass of alpha-quazi Spirallike Mappings

Melike Aydogan

he open unit disc D = {z ∈ C : |z| < 1}. A sense preserving logharmonic mapping is the solution of the non-linear elliptic partial differantial equation f z = w(z)fz( f f ) where w(z) ∈ H(D) is the second dilatation of f such that |w(z)| < 1 for all z ∈ D. It has been shown that if f is a non-vanishing logharmonic mapping, then f can be expressed as f(z) = h(z).g(z), where h(z) and g(z) are analytic in D with the normalization h(0) 6= 0, g(0) = 1. If f vanishes at z = 0 but it is not identically zero, then f admits the representation f = z. |z| 2β h(z)g(z), where Reβ > − 1 2 and h(z), g(z) are analytic in D with the normalization h(0) 6= 0, g(0) = 1. [1], [2], [3]. The class of all logharmonic mappings is denoted by S ∗ LH. The aim of this paper is to give an aplication of the subordination principle to the class of spirallike logharmonic mappings which was introduced by Z.Abdulhadi and W.Hengartner.