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Landau-type theorems for certain bounded bi-analytic functions and biharmonic mappings
Part of
- Two-dimensional theory
- Geometric function theory
Ming-Sheng Liu, Saminathan Ponnusamy
Journal:

Canadian Mathematical Bulletin / Volume 67 / Issue 1 / March 2024

Published online by Cambridge University Press:

05 July 2023, pp. 152-165

Print publication:

March 2024
- Article
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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.