Article ID: MTJPAM-D-20-00032

Title: Connections between Various Subclasses of Uniformly Harmonic Starlike Mappings and Poisson Distribution Series

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-20-00032; Volume 3 / Issue 3 / Year 2021 (Special Issue), Pages 297-304

Document Type: Research Paper

Author(s): Rabha Mohamad El-Ashwah a , Wafaa Yahia Kota b

aDepartment of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt

bDepartment of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt

Received: 27 September 2020, Accepted: 28 March 2021, Published: 25 April 2021.

Corresponding Author: Rabha Mohamad El-Ashwah (Email address:

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In this paper, we use a power series with coefficients are the probabilities of Poisson distribution and obtain sufficient conditions for this power series and some related series to be in various subclasses of harmonic functions. Also, we investigate several mapping properties involving these subclasses.

Keywords: Harmonic starlike, Harmonic ɣ-uniformly starlike, Poisson distribution series, Univalent functions

  1. O. P. Ahuja, Planar harmonic univalent and related mappings, J. Ineq. Pure Appl. Math. 6 (4), Article 122, 1-8, 2005.
  2. O. P. Ahuja, R. Aghalary and S. B. Joshi, Harmonic univalent functions associated with k-uniformly starlike functions, Math. Sci. Res. J. 9 (1), 9-17, 2005.
  3. O. P. Ahuja and J. M. Jahangiri, Noshiro-type harmonic univalent functions, Sci. Math. Jpn. 6 (2), 253-259, 2002.
  4. J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fen. Series A. I. Math. 9, 3-25, 1984.
  5. P. L. Duren, Harmonic Mappings in the Plane, Cambridge Tracts in Mathematics, Cambridge University Press, Vol. 156, 2004, ISBN 0-521-64121-7.
  6. J. M. Jahangiri, Harmonic functions starlike in the unit disk, J. Math. Anal. Appl. 235, 470-477, 1999.
  7. S. Porwal, An application of a Poisson distribution series on certain analytic functions, J. Complex Anal. Art. ID 984135, pp. 3, 2014.
  8. S. Porwal and D. Srivastava, Some connections between various subclasses of planar harmonic mappings involving Poisson distribution series, Electron J. Math. Anal. Appl. 6 (2), 163-171, 2018.
  9. F. Rønning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. 118 (1), 189-196, 1993.
  10. T. Rosy, B. A. Stephen, K. G. Subramanian and J. M. Jahangiri, Goodman-Ronning-type harmonic univalent functions, Kyungpook Math. J. 41 (1), 45-54, 2001.
  11. H. Silverman, Harmonic univalent functions with negative coefficients, J. Math. Anal. Appl. 220, 283-289, 1998.