Abstract
This paper treats the class of normalized logharmonic mappings f(z) = zh(z)<(g(z))over bar>in the unit disk satisfying phi(z) = zh(z)g(z) is analytically typically real. Every such mapping f admits an integral representation in terms of its second dilatation function and a function of positive real part with real coefficients. The radius of starlikeness and an upper estimate for arclength are obtained. Additionally, it is shown that f maps the unit disk into a domain symmetric with respect to the real axis when its second dilatation has real coefficients.