Landau's theorems for biharmonic mappings (II)

Liu, Ming-Sheng; Xie, Li; Yang, Li-Mei

doi:10.1002/mma.4183

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Landau and Bloch Theorems1

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2018

2023

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Cited by 9 publications

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“…In 2008, Abdulhadi and Muhanna established two versions of Landau-type theorems for certain bounded biharmonic mappings in [2]. For later developments on this topic, we refer to [8,9,17,20,22,26]. In particular, sharp versions of Theorem B have been established in [15,18,19], and the corresponding sharp versions of Landau-type theorems for normalized bounded biharmonic mappings have also been established in [21].…”

Section: Landau and Bloch Theoremsmentioning

confidence: 99%

Landau-type theorems for certain bounded bi-analytic functions and biharmonic mappings

Liu¹,

Ponnusamy²

2023

Can. Math. Bull.

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In this article, we establish three new versions of Landau-type theorems for bounded bi-analytic functions of the form $F(z)=\bar {z}G(z)+H(z)$ , where G and H are analytic in the unit disk with $G(0)=H(0)=0$ and $H'(0)=1$ . In particular, two of them are sharp, while the other one either generalizes or improves the corresponding result of Abdulhadi and Hajj. As consequences, several new sharp versions of Landau-type theorems for certain subclasses of bounded biharmonic mappings are proved.

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