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Landau–Bloch Type Theorems for Certain Subclasses for Polyharmonic Mappings

Landau–Bloch Type Theorems for Certain Subclasses for Polyharmonic Mappings In this paper, we first establish a Landau–Bloch type theorem for certain bounded polyharmonic mappings, which improves upon a result given by Bai et al. (Complex Anal Oper Theory, 13(2):321–340, 2019). Then, we establish three new versions of Landau–Bloch type theorems for polyharmonic mappings, and obtain several sharp results. Finally, we provide four bi-Lipschitz theorems for these subclasses of polyharmonic mappings. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Landau–Bloch Type Theorems for Certain Subclasses for Polyharmonic Mappings

Computational Methods and Function Theory , Volume OnlineFirst – May 16, 2022

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-022-00441-9
Publisher site
See Article on Publisher Site

Abstract

In this paper, we first establish a Landau–Bloch type theorem for certain bounded polyharmonic mappings, which improves upon a result given by Bai et al. (Complex Anal Oper Theory, 13(2):321–340, 2019). Then, we establish three new versions of Landau–Bloch type theorems for polyharmonic mappings, and obtain several sharp results. Finally, we provide four bi-Lipschitz theorems for these subclasses of polyharmonic mappings.

Journal

Computational Methods and Function TheorySpringer Journals

Published: May 16, 2022

Keywords: Landau–Bloch type theorem; Bi-Lipschitz theorem; Harmonic mapping; Polyharmonic mapping; Univalent; Primary 30C99; Secondary 30C62; 30C25

References