In this paper, we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the form $L(f)=z f_z-\bar{z} f_{\bar{z}}$, where $f$ represents normalized harmonic mappings with bounded dilation. Then, using these results, we present better estimations for the Bloch constants of certain harmonic mappings $L(f)$, where $f$ is a $K$-quasiregular harmonic or open harmonic. Finally, we establish three versions of Bloch-Landau type theorem for biharmonic mappings of the form $L(f)$. These results are sharp in some given cases and improve the related results of earlier authors.
Jieling Chen
,
Mingsheng Liu
. ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR*[J]. Acta mathematica scientia, Series B, 2024
, 44(1)
: 295
-310
.
DOI: 10.1007/s10473-024-0116-0
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