Landau-type Theorems for Polyanalytic and Log-$α$-analytic functions
P. Li, M. -S. Liu, S. Ponnusamy, H. Zhao
公開日: 2025/10/3
Abstract
In the present article, we investigate the univalence property of polyanalytic functions and $\log$-$\alpha$-analytic functions. First, by using a new idea, we prove an improved lemma and the coefficient estimates for bounded polyanalytic functions on the unit disk. Then, we present three versions of Landau-type theorems for such functions and determine the univalence domain and the radius of schlicht disk. Finally, as a consequence, the Landau-type theorems for $\log$-$\alpha$-analytic functions are also provided.