Some inequalities which hold for starlike log-harmonic mappings of order ?

where w(z) ? H(D) is second dilatation such that |w(z)| < 1 for all z ? D. It has been shown that if f is a non-vanishing log-harmonic mapping, then f can be expressed as (Formula presented)Let H(D) be the linear space of all analytic functions defined on the open disc D = {z| |z| < 1}. A log-harmonic mappings is a solution of the nonlinear elliptic partial differential equation (Formula presented)where h(z) and g(z) are analytic function in D. On the other hand, if f vanishes at z = 0 but it is not identically zero then f admits following representation (Formula presented)where Re(Formula presented) , h and g are analytic in D, g(0) = 1, h(0) ? 0. Let 2 f = z |z|2ß hg be a univalent log-harmonic mapping. © 2014 by Eudoxus Press,LLC,all rights reserved.