TY - JOUR
T1 - Improved Bohr's inequality for locally univalent harmonic mappings
AU - Evdoridis, Stavros
AU - Ponnusamy, Saminathan
AU - Rasila, Antti
N1 - Publisher Copyright:
© 2018 Royal Dutch Mathematical Society (KWG)
PY - 2019/1
Y1 - 2019/1
N2 - We prove several improved versions of Bohr's inequality for the harmonic mappings of the form [Formula presented], 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 [Formula presented] 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.
AB - We prove several improved versions of Bohr's inequality for the harmonic mappings of the form [Formula presented], 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 [Formula presented] 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.
KW - Bounded analytic functions
KW - Harmonic functions
KW - Locally univalent functions and Bohr radius
UR - http://www.scopus.com/inward/record.url?scp=85055086607&partnerID=8YFLogxK
U2 - 10.1016/j.indag.2018.09.008
DO - 10.1016/j.indag.2018.09.008
M3 - 文章
AN - SCOPUS:85055086607
SN - 0019-3577
VL - 30
SP - 201
EP - 213
JO - Indagationes Mathematicae
JF - Indagationes Mathematicae
IS - 1
ER -