November 8, 2025Open Access

Landau-type Theorems for Polyanalytic and Log-α-analytic functions

Key Points

Polyanalytic functions show important univalence properties on the unit disk, enhancing our understanding of their behavior.
Key findings include coefficient estimates that define bounded polyanalytic functions and their implications for univalence.
Exploration of Landau-type theorems demonstrates new insights into the domains and behaviors of polyanalytic and log-α-analytic functions.
Supports broader applications of analytic functions, highlighting their potential in complex analysis and mathematical modeling.

Abstract

In the present article, we investigate the univalence property of polyanalytic functions and -α-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 -α-analytic functions are also provided.

Landau-type Theorems for Polyanalytic and Log-α-analytic functions

Key Points

Abstract

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