On Landau-Type Theorems for Poly-Analytic Functions
Vasudevarao Allu, Rohit Kumar
TL;DR
This paper extends Landau-type theorems to bounded poly-analytic functions and proves bi-Lipschitz properties for specific subclasses, broadening understanding of their geometric behavior.
Contribution
It introduces new Landau-type and bi-Lipschitz theorems for bounded poly-analytic functions, generalizing previous results for bi-analytic functions.
Findings
Established three Landau-type theorems for bounded poly-analytic functions.
Proved three bi-Lipschitz theorems for subclasses of poly-analytic functions.
Generalized previous results for bi-analytic functions to poly-analytic functions.
Abstract
In this paper, we establish three Landau-type theorems for certain bounded poly-analytic functions, which generalize the corresponding result for bi-analytic functions given by Liu and Ponnusamy [Canad. Math. Bull. 67(1): 2024, 152-165]. Further, we prove three bi-Lipschitz theorems for these subclasses of poly-analytic functions.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Mathematical Analysis and Transform Methods