Landau's theorems for certain biharmonic mappings
Ming-Sheng Liu, Zhi-Wen Liu, Yu-Can Zhu
TL;DR
This paper establishes sharp coefficient estimates for bounded harmonic mappings and applies these results to improve Landau's theorems for certain biharmonic mappings, refining previous findings.
Contribution
It provides new sharp coefficient bounds for harmonic mappings and enhances Landau's theorems for biharmonic mappings, advancing the theoretical understanding.
Findings
Sharp coefficient estimates for bounded harmonic mappings
Refined Landau's theorems for biharmonic mappings
Improved bounds compared to earlier results
Abstract
Let be a harmonic mapping of the unit disk . In this paper, the sharp coefficient estimates for bounded planar harmonic mappings are established, the sharp coefficient estimates for normalized planar harmonic mappings with are also provided. As their applications, Landau's theorems for certain biharmonic mappings are provided, which improve and refine the related results of earlier authors.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Differential Equations and Boundary Problems