# Polyharmonic functions with negative coefficients

Volume 17, Issue 4, pp 437-447

Publication Date: 2017-08-27

http://dx.doi.org/10.22436/jmcs.017.04.01

### 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.