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Some Properties of Harmonic Functions Defined by Convolution

Dixit, Kaushal Kishor;Porwal, Saurabh

  • Received : 2009.02.01
  • Accepted : 2009.06.03
  • Published : 2009.12.31

Abstract

In this paper, we introduce and study a comprehensive family of harmonic univalent functions which contains various well-known classes of harmonic univalent functions as well as many new ones. Also, we improve some results obtained by Frasin [3] and obtain coefficient bounds, distortion bounds and extreme points, convolution conditions and convex combination are also determined for functions in this family. It is worth mentioning that many of our results are either extensions or new approaches to those corresponding previously known results.

Keywords

harmonic;analytic and univalent functions

References

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Cited by

  1. Partial sums of certain harmonic univalent functions vol.32, pp.4, 2011, https://doi.org/10.1134/S1995080211040184
  2. Some properties of a subclass of harmonic univalent functions defined by the multiplier transformations vol.46, pp.3, 2015, https://doi.org/10.1007/s13226-015-0132-9
  3. A Convolution Approach on Partial Sums of Certain Harmonic Univalent Functions vol.2012, 2012, https://doi.org/10.1155/2012/509349