Geodesic
Landau-Bloch type theorems of certain subclasses of biharmonic mappings
Filomat, Tome 37 (2023) no. 2, p. 403

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DOI

In this paper, we first establish a Landau-Bloch type theorem for certain bounded and normalized biharmonic mappings F(z) = |z| 2 (z) + h(z), where (z) and h(z) are harmonic in the unit disk with |(z)| ≤ M 1 , |h(z)| ≤ M 2. In particular, our result is sharp when M 1 = M 2 = 1. Then, we establish several new versions of Landau-Bloch type theorems for certain normalized biharmonic mappings with the coefficients condition in place of |h(z)| ≤ M 2 or |(z)| ≤ M 1 , and obtain several sharp results.
DOI : 10.2298/FIL2302403L
Classification : 30C99, 30C62
Keywords: Landau-Bloch type theorem, Harmonic mapping, Biharmonic mapping, Univalent 
Xi Luo; Ming-Sheng Liu; Ting Li. Landau-Bloch type theorems of certain subclasses of biharmonic mappings. Filomat, Tome 37 (2023) no. 2, p. 403 . doi: 10.2298/FIL2302403L
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     author = {Xi Luo and Ming-Sheng Liu and Ting Li},
     title = {Landau-Bloch type theorems of certain subclasses of biharmonic mappings},
     journal = {Filomat},
     pages = {403 },
     year = {2023},
     volume = {37},
     number = {2},
     doi = {10.2298/FIL2302403L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2302403L/}
}
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