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Harmonic k-Uniformly Convex, k-Starlike Mappings and Pascal Distribution Series

Year 2020, , 1 - 9, 15.10.2020
https://doi.org/10.36753/mathenot.683486

Abstract

In this paper, connections between various subclasses of harmonic univalent
functions by using a convolution operator involving the Pascal distribution
series are investigated. Furthermore, an example is provided, illustrating graphically with the help
of Maple, to illuminate the convolution operator.                                               .................................................................................................................................                                                                                                     

References

  • [1] Ahuja, O.P., Aghalary, R., Joshi, S.B.: Harmonic univalent functions associated with k-uniformly starlike functions. Math. Sci. Res. J. 9 (1), 9-17 (2005).
  • [2] Clunie, J., Sheil-Small, T.: Harmonic univalent functions. Ann. Acad. Sci. Fenn. Ser. A I Math. 9, 3-25 (1984).
  • [3] Duren, P.: Harmonic Mappings in the Plane. Cambridge University Press. Cambridge (2004).
  • [4] Goodman, A.W.: On uniformly convex functions. Ann. Polon. Math. 56 (1), 87-92 (1991).
  • [5] Kim, Y.C., Jahangiri, J.M., Choi, J.H.: Certain convex harmonic functions. Int. J. Math. Sci. 29 (8), 459-465 (2002).
  • [6] Rønning, F.: Uniformly convex functions and a corresponding class of starlike functions. Proc. Amer. Math. Soc. 118, 189-196 (1993).
  • [7] Rosy, T., Stephen, B.A., Subramanian, K.G., Jahangiri, J.M.: Goodman-Rønning-type harmonic univalent functions. Kyungpook Math. J. 41(1) 45-54 (2001).
  • [8] Altınkaya, ¸S., Yalçın, S.: Poisson Distribution Series for Certain Subclasses of Starlike Functions with Negative Coefficients. Annals of Oradea University Mathematics Fascicola 2. 24 (2), 5-8 (2017).
  • [9] Porwal, S., Kumar, M.: A unified study on starlike and convex functions associated with Poisson distribution series. Afrika Matematika. 27 (5-6), 1021-1027 (2016).
  • [10] Porwal, S.: An application of a Poisson distribution series on certain analytic functions. J. Complex Anal. Article ID 984135, 1-3 (2014).
  • [11] Nazeer, W., Mehmood, Q., Kang, S.M., Haq, A.U.: An application of Binomial distribution series on certain analytic functions. Journal of Computational Analysis and Applications. 26 (1), 11-17 (2019).
  • [12] Çakmak, S., Yalçin, S., Altınkaya, ¸S.: Some connections between various classes of analytic functions associated with the power series distribution. Sakarya Univ. Jour. Science. 23 (5), 982-985 (2019).
  • [13] El-Deeb, M.S., Bulboaca, T., Dziok, J.: Pascal Distribution Series connected with certain subclasses of univalent functions. Kyunpook Math. J. 59, 301-314 (2019).
Year 2020, , 1 - 9, 15.10.2020
https://doi.org/10.36753/mathenot.683486

Abstract

References

  • [1] Ahuja, O.P., Aghalary, R., Joshi, S.B.: Harmonic univalent functions associated with k-uniformly starlike functions. Math. Sci. Res. J. 9 (1), 9-17 (2005).
  • [2] Clunie, J., Sheil-Small, T.: Harmonic univalent functions. Ann. Acad. Sci. Fenn. Ser. A I Math. 9, 3-25 (1984).
  • [3] Duren, P.: Harmonic Mappings in the Plane. Cambridge University Press. Cambridge (2004).
  • [4] Goodman, A.W.: On uniformly convex functions. Ann. Polon. Math. 56 (1), 87-92 (1991).
  • [5] Kim, Y.C., Jahangiri, J.M., Choi, J.H.: Certain convex harmonic functions. Int. J. Math. Sci. 29 (8), 459-465 (2002).
  • [6] Rønning, F.: Uniformly convex functions and a corresponding class of starlike functions. Proc. Amer. Math. Soc. 118, 189-196 (1993).
  • [7] Rosy, T., Stephen, B.A., Subramanian, K.G., Jahangiri, J.M.: Goodman-Rønning-type harmonic univalent functions. Kyungpook Math. J. 41(1) 45-54 (2001).
  • [8] Altınkaya, ¸S., Yalçın, S.: Poisson Distribution Series for Certain Subclasses of Starlike Functions with Negative Coefficients. Annals of Oradea University Mathematics Fascicola 2. 24 (2), 5-8 (2017).
  • [9] Porwal, S., Kumar, M.: A unified study on starlike and convex functions associated with Poisson distribution series. Afrika Matematika. 27 (5-6), 1021-1027 (2016).
  • [10] Porwal, S.: An application of a Poisson distribution series on certain analytic functions. J. Complex Anal. Article ID 984135, 1-3 (2014).
  • [11] Nazeer, W., Mehmood, Q., Kang, S.M., Haq, A.U.: An application of Binomial distribution series on certain analytic functions. Journal of Computational Analysis and Applications. 26 (1), 11-17 (2019).
  • [12] Çakmak, S., Yalçin, S., Altınkaya, ¸S.: Some connections between various classes of analytic functions associated with the power series distribution. Sakarya Univ. Jour. Science. 23 (5), 982-985 (2019).
  • [13] El-Deeb, M.S., Bulboaca, T., Dziok, J.: Pascal Distribution Series connected with certain subclasses of univalent functions. Kyunpook Math. J. 59, 301-314 (2019).
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Elif Yaşar 0000-0003-0176-4961

Publication Date October 15, 2020
Submission Date February 2, 2020
Acceptance Date April 10, 2020
Published in Issue Year 2020

Cite

APA Yaşar, E. (2020). Harmonic k-Uniformly Convex, k-Starlike Mappings and Pascal Distribution Series. Mathematical Sciences and Applications E-Notes, 8(2), 1-9. https://doi.org/10.36753/mathenot.683486
AMA Yaşar E. Harmonic k-Uniformly Convex, k-Starlike Mappings and Pascal Distribution Series. Math. Sci. Appl. E-Notes. October 2020;8(2):1-9. doi:10.36753/mathenot.683486
Chicago Yaşar, Elif. “Harmonic K-Uniformly Convex, K-Starlike Mappings and Pascal Distribution Series”. Mathematical Sciences and Applications E-Notes 8, no. 2 (October 2020): 1-9. https://doi.org/10.36753/mathenot.683486.
EndNote Yaşar E (October 1, 2020) Harmonic k-Uniformly Convex, k-Starlike Mappings and Pascal Distribution Series. Mathematical Sciences and Applications E-Notes 8 2 1–9.
IEEE E. Yaşar, “Harmonic k-Uniformly Convex, k-Starlike Mappings and Pascal Distribution Series”, Math. Sci. Appl. E-Notes, vol. 8, no. 2, pp. 1–9, 2020, doi: 10.36753/mathenot.683486.
ISNAD Yaşar, Elif. “Harmonic K-Uniformly Convex, K-Starlike Mappings and Pascal Distribution Series”. Mathematical Sciences and Applications E-Notes 8/2 (October 2020), 1-9. https://doi.org/10.36753/mathenot.683486.
JAMA Yaşar E. Harmonic k-Uniformly Convex, k-Starlike Mappings and Pascal Distribution Series. Math. Sci. Appl. E-Notes. 2020;8:1–9.
MLA Yaşar, Elif. “Harmonic K-Uniformly Convex, K-Starlike Mappings and Pascal Distribution Series”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 2, 2020, pp. 1-9, doi:10.36753/mathenot.683486.
Vancouver Yaşar E. Harmonic k-Uniformly Convex, k-Starlike Mappings and Pascal Distribution Series. Math. Sci. Appl. E-Notes. 2020;8(2):1-9.

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