Polyharmonic functions with negative coefficients

Volume 17, Issue 4, pp 437-447 http://dx.doi.org/10.22436/jmcs.017.04.01

Publication Date: August 27, 2017 Submission Date: February 16, 2016

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2686 Downloads
• 3874 Views

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.

Share and Cite

Keywords

• Univalent functions
• polyharmonic mappings
• extreme points.

MSC

•  30C45
•  30C50

References

• [1] Y. Avci, E. Zlotkiewicz, On harmonic univalent mappings, Ann. Univ. Mariae Curie-Skodowska Sect. A, 44 (1990), 1–7.


• [2] J. Clunie, T. Shell-Small, Harmonic univalent functions, Ann. Acad. Aci. Fenn. Ser. A I Math., 9 (1984), 3–25.
  • Google Scholar


• [3] J. M. Jahangiri, Coefficient bounds and univalence criteria for harmonic functions with negative coefficients, Ann. Univ. Mariae Curie Sklodowska Sect A., 52 (1998), 57–66.
  • MathSciNet
  • Google Scholar
  • MATH


• [4] J. M. Jahangiri, Harmonic functions starlike in the unit disk, J. Math. Anal. Appl., 235 (1999), 470–477.
  • View Article
  • MathSciNet
  • Google Scholar


• [5] J. Qiao, X. Wang, On p-harmonic univalent mapping, Acta Math. Sci. A, 32 (2012), 588–600.


• [6] H. Silverman , Harmonic univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51 (1998), 283–289.
  • View Article
  • Google Scholar


• [7] H. Silverman, E. M. Silvia, Subclasses of harmonic univalent functions, New Zealand J. Math., 28 (1999), 275–284.
  • Google Scholar