Abstract
We prove several improved versions of Bohr’s inequality for the harmonic mappings of the form f=h+g¯, where h is bounded by 1 and |g′(z)|≤|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.
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