Polyharmonic functions with negative coefficients


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.


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