Abstract
We prove several improved versions of Bohr’s inequality for the harmonic mappings of the form f=h+\overline{g}, where h is bounded by 1 and |g'(z)| \leq |h'(z)|.
The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. (Kayumov and Ponnusamy, 2018) for example a term related to the area of the image of the disk D(0,r) under the mapping f is considered. Our results are sharp. In addition, further improvements of the main results for certain special classes of harmonic mappings are provided.
The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. (Kayumov and Ponnusamy, 2018) for example a term related to the area of the image of the disk D(0,r) under the mapping f is considered. Our results are sharp. In addition, further improvements of the main results for certain special classes of harmonic mappings are provided.
| Original language | English |
|---|---|
| Pages (from-to) | 201-213 |
| Journal | Indagationes Mathematicae: New Series |
| Volume | 30 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 9 Oct 2018 |
| MoE publication type | A1 Journal article-refereed |