Abstract
We determine the representation theorem, distortion theorem, coefficients estimate and Bohr?s radius for log-harmonic starlike mappings of order ?, which are generalization of some earlier results. In addition, the inner mapping radius of log-harmonic mappings is also established by constructing a family of 1-slit log-harmonic mappings. Finally, we introduce pre-Schwarzian, Schwarzian derivatives and Bloch?s norm for non-vanishing log-harmonic mappings, several properties related to these are also obtained.
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