Properties of Harmonic Functions Defined by Shear Construction

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.

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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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Correspondence to Rasoul Aghalary.

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Aghalary, R., Rad, M.J. Properties of Harmonic Functions Defined by Shear Construction. Acta Math Vietnam 43, 471–483 (2018). https://doi.org/10.1007/s40306-017-0235-y

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Keywords

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

Mathematics Subject Classification (2010)

  • Primary 30C45
  • Secondary 30C80