Landau's theorem for polyharmonic mappings
Jiaolong Chen, Antti Rasila, Xiantao Wang
TL;DR
This paper extends Landau's theorem to polyharmonic mappings in the unit disk, providing coefficient estimates and new bounds for these complex functions, along with examples and numerical analysis.
Contribution
It introduces two versions of Landau's theorem for polyharmonic mappings and their derivatives, advancing the theoretical understanding of these functions.
Findings
Coefficient estimates for bounded polyharmonic mappings
Two versions of Landau's theorem established
Examples and numerical estimates provided
Abstract
In this paper, we first investigate coefficient estimates for bounded polyharmonic mappings in the unit disk . Then, we obtain two versions of Landau's theorem for polyharmonics mapping , and for the mappings of the type , where is the differential operator of Abdulhadi, Abu Muhanna and Khuri. Examples and numerical estimates are given.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Meromorphic and Entire Functions