Some properties of univalent log-harmonic mappings

ZhiHong Liu; Saminathan Ponnusamy

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arXiv · 1808.07393

Some properties of univalent log-harmonic mappings

ZhiHong Liu·Saminathan Ponnusamy

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Abstract

We determine the representation theorem, distortion theorem, coefficients estimate and Bohr's radius for log-harmonic starlike mappings of order $\alpha$, 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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ZhiHong Liu, Saminathan Ponnusamy. 2018-08-22. Some properties of univalent log-harmonic mappings. https://arxiv.org/abs/1808.07393

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