Abstract
In this note, we introduce a general class of sense-preserving harmonic mappings defined as follows:
where \(h(z)=z+\sum _{m=2}^{\infty }a_mz^m\), \(g(z)=\sum _{m=2}^{\infty }b_m z^m\) are analytic functions in \(\mathbb {D}:=\{z\in \mathbb {C}: |z|\le 1 \}\) and
for all \(m\ge 2\). We obtain Growth Theorem, Covering Theorem, and derive the Bohr radius for the class \(\mathcal {B}_{\mathcal {H}}^{0}(M)\). As an application of our results, we obtain the Bohr radius for many classes of harmonic univalent functions and some classes of univalent functions.
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We are thankful to the Editor and the Reviewers for their valuable suggestions to improve the previous version of this manuscript.
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The work of Kamajeet Gangania is supported by University Grant Commission, New-Delhi, India under UGC-Ref. No.:1051/(CSIR-UGC NET JUNE 2017).
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The work of Kamajeet Gangania is supported by University Grant Commission, New-Delhi, India under UGC-Ref. No.:1051/(CSIR-UGC NET JUNE 2017)
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Gangania, K., Kumar, S.S. Bohr Radius for Some Classes of Harmonic Mappings. Iran J Sci Technol Trans Sci 46, 883–890 (2022). https://doi.org/10.1007/s40995-022-01304-7
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DOI: https://doi.org/10.1007/s40995-022-01304-7