Landau-type Theorems for Polyanalytic and Log-$\hat{I}\pm$-analytic functions

Abstract

In the present article, we investigate the univalence property of polyanalytic functions and $\log$-$\hat{I}\pm$-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 $\log$-$\hat{I}\pm$-analytic functions are also provided.

18 pages; To appear in the Journal of Mathematical Analysis and Applications