# Polyharmonic functions with negative coefficients

Volume 17, Issue 4, pp 437-447 Publication Date: August 27, 2017       Article History
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### Authors

K. Al-Shaqsi - Department of Information Technology, Nizwa College of Technology, Ministry of Manpower, Sultanate of Oman R. Al-Khal - Department of Mathematics, Sciences College, University of Dammam, Dammam, Saudi Arabia

### Abstract

A 2p times continuously differentiable complex-valued mapping $F=u+i v$ in a domain $\mathcal D \subset \mathbb C$ is polyharmonic if $F$ satisfies the polyharmonic equation $\underbrace{\Delta\cdot\cdot\cdot\Delta}_\text{p} F= 0$, where $p \in \mathbb N^{+}$ and $\Delta$ represents the complex Laplacian operator. The main aim of this paper is to introduce a subclasses of polyharmonic mappings. Coefficient conditions, distortion bounds, extreme points, of the subclasses are obtained.

### Keywords

• Univalent functions
• polyharmonic mappings
• extreme points.

•  30C45
•  30C50

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