Polyharmonic functions with negative coefficients


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


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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ISRP Style

K. Al-Shaqsi, R. Al-Khal, Polyharmonic functions with negative coefficients, Journal of Mathematics and Computer Science, 17 (2017), no. 4, 437-447

AMA Style

Al-Shaqsi K., Al-Khal R., Polyharmonic functions with negative coefficients. J Math Comput SCI-JM. (2017); 17(4):437-447

Chicago/Turabian Style

Al-Shaqsi, K., Al-Khal, R.. "Polyharmonic functions with negative coefficients." Journal of Mathematics and Computer Science, 17, no. 4 (2017): 437-447