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Acta Mathematica Vietnamica

, Volume 43, Issue 3, pp 471–483 | Cite as

Properties of Harmonic Functions Defined by Shear Construction

  • Rasoul Aghalary
  • Mahdi Jahani Rad
Article
  • 36 Downloads

Abstract

In this paper, we introduce a new subclass of harmonic functions defined by shear construction. Among other properties of this subclass, we study the convolution of its elements of it with some special subclasses of harmonic functions. Also, we provide coefficient conditions leading to harmonic mappings which are starlike of order \(\alpha \). Some interesting applications of the general results are also presented.

Keywords

Harmonic starlike and convex functions Shear construction Univalent harmonic function Radii problem 

Mathematics Subject Classification (2010)

Primary 30C45 Secondary 30C80 

Notes

Acknowledgements

The authors would like to thank the referees for their careful reading of the paper and for their helpful comments to improve it.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceUrmia UniversityUrmiaIran

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