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Subclasses of analytic functions associated with Pascal distribution series

Year 2020, , 92 - 99, 30.06.2020
https://doi.org/10.31197/atnaa.692948

Abstract

In the present paper, we determine necessary and sufficient conditions for the Pascal distribution series to be in the subclasses S(k,λ) and C(k,λ) of analytic functions. Further, we consider an integral operator related to Pascal distribution series. Some interesting special cases of our main results are also considered.

References

  • References [1] R. M. El-Ashwah and W. Y Kota, Some condition on a Poisson distribution series to be in subclasses of univalent functions, Acta Universitatis Apulensis, No. 51/2017, pp. 89-103.
  • [2] S.Çakmak, S.Yalç¬n, and ¸S. Alt¬nkaya, Some connections between various classes of analytic functions associated with the power series distribution, Sakarya Univ. J. Sci., 23(5)(2019), 982–985.
  • [3] N. E. Cho, S. Y. Woo and S. Owa, Uniform convexity properties for hypergeometric functions, Fract. Cal. Appl. Anal., 5(3) (2002), 303–313.
  • [4] S. M. El-Deeb, T. Bulboac¼a and J. Dziok, Pascal distribution series connected with certain subclasses of univalent functions, Kyungpook Math. J. 59(2019), 301–314.
  • [5] K.K. Dixit and S.K. Pal, On a class of univalent functions related to complex order, Indian J. Pure Appl. Math., 26(1995), no. 9, 889-896.
  • [6] B.A. Frasin, On certain subclasses of analytic functions associated with Poisson distribution series, Acta Universitatis Sapientiae Mathematica 11, 1 (2019) 78–86.
  • [7] B.A. Frasin, Tariq Al-Hawary and Feras Yousef, Necessary and su¢ cient conditions for hypergeometric functions to be in a subclass of analytic functions, Afrika Matematika, Volume 30, Issue 1–2, 2019, pp. 223–230.
  • [8] B. A. Frasin and Ibtisam Aldawish, On subclasses of uniformly spirallike functions associated with generalized Bessel functions, Journal of Function Spaces, Volume 2019, Article ID 1329462, 6 pages.
  • [9] W. Nazeer, Q. Mehmood, S.M. Kang, and A. Ul Haq, An application of Binomial distribution series on certain analytic functions, J. Computational Analysis and Applications. Volume 26,No.1(2019),11-17.
  • [10] E. Merkes and B. T. Scott, Starlike hypergeometric functions, Proc. Amer. Math. Soc., 12 (1961), 885-888.
  • [11] M.L. Mogra, On a class of starlike functions in the unit disc I, J. Indian Math. Soc. 40(1976), 159-161.
  • [12] G. Murugusundaramoorthy, Subclasses of starlike and convex functions involving Poisson distribution series, Afr. Mat. (2017) 28:1357-1366.
  • [13] G. Murugusundaramoorthy, K. Vijaya and S. Porwal, Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series, Hacettepe J. Math. Stat. 45(2016), no. 4, 1101-1107.
  • [14] G. Murugusundaramoorthy, B. A. Frasin and Tariq Al-Hawary, Uniformly convex spiral functions and uniformly spirallike function associated with Pascal distribution series, arXiv:2001.07517 [math.CV].
  • [15] A. T. Oladipo, Bounds for probability of the generalised distribution defined by generalised polylog- arithm, Punjab University, Journal of Mathematics, Vol 51(7) (2019), 19-26.
  • [16] S. Owa, On certain classes of univalent functions in the unit disc, Kyungpook Math. J., Vol. 24, No. 2 (1984), 127-136.
  • [17] K.S. Padmanabhan, On certain classes of starlike functions in the unit disc, J. Indian Math. Soc. 32(1968), 89-103.
  • [18] S. Porwal, An application of a Poisson distribution series on certain analytic functions, J. Complex Anal., (2014), Art. ID 984135, 1–3.
  • [19] H. Silverman, Starlike and convexity properties for hypergeometric functions, J. Math. Anal. Appl. 172 (1993), 574–581.
  • [20] H. M. Srivastava, G. Murugusundaramoorthy and S. Sivasubramanian, Hypergeometric functions in the parabolic starlike and uniformly convex domains, Integr. Transf. Spec. Func. 18 (2007), 511–520.
Year 2020, , 92 - 99, 30.06.2020
https://doi.org/10.31197/atnaa.692948

Abstract

References

  • References [1] R. M. El-Ashwah and W. Y Kota, Some condition on a Poisson distribution series to be in subclasses of univalent functions, Acta Universitatis Apulensis, No. 51/2017, pp. 89-103.
  • [2] S.Çakmak, S.Yalç¬n, and ¸S. Alt¬nkaya, Some connections between various classes of analytic functions associated with the power series distribution, Sakarya Univ. J. Sci., 23(5)(2019), 982–985.
  • [3] N. E. Cho, S. Y. Woo and S. Owa, Uniform convexity properties for hypergeometric functions, Fract. Cal. Appl. Anal., 5(3) (2002), 303–313.
  • [4] S. M. El-Deeb, T. Bulboac¼a and J. Dziok, Pascal distribution series connected with certain subclasses of univalent functions, Kyungpook Math. J. 59(2019), 301–314.
  • [5] K.K. Dixit and S.K. Pal, On a class of univalent functions related to complex order, Indian J. Pure Appl. Math., 26(1995), no. 9, 889-896.
  • [6] B.A. Frasin, On certain subclasses of analytic functions associated with Poisson distribution series, Acta Universitatis Sapientiae Mathematica 11, 1 (2019) 78–86.
  • [7] B.A. Frasin, Tariq Al-Hawary and Feras Yousef, Necessary and su¢ cient conditions for hypergeometric functions to be in a subclass of analytic functions, Afrika Matematika, Volume 30, Issue 1–2, 2019, pp. 223–230.
  • [8] B. A. Frasin and Ibtisam Aldawish, On subclasses of uniformly spirallike functions associated with generalized Bessel functions, Journal of Function Spaces, Volume 2019, Article ID 1329462, 6 pages.
  • [9] W. Nazeer, Q. Mehmood, S.M. Kang, and A. Ul Haq, An application of Binomial distribution series on certain analytic functions, J. Computational Analysis and Applications. Volume 26,No.1(2019),11-17.
  • [10] E. Merkes and B. T. Scott, Starlike hypergeometric functions, Proc. Amer. Math. Soc., 12 (1961), 885-888.
  • [11] M.L. Mogra, On a class of starlike functions in the unit disc I, J. Indian Math. Soc. 40(1976), 159-161.
  • [12] G. Murugusundaramoorthy, Subclasses of starlike and convex functions involving Poisson distribution series, Afr. Mat. (2017) 28:1357-1366.
  • [13] G. Murugusundaramoorthy, K. Vijaya and S. Porwal, Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series, Hacettepe J. Math. Stat. 45(2016), no. 4, 1101-1107.
  • [14] G. Murugusundaramoorthy, B. A. Frasin and Tariq Al-Hawary, Uniformly convex spiral functions and uniformly spirallike function associated with Pascal distribution series, arXiv:2001.07517 [math.CV].
  • [15] A. T. Oladipo, Bounds for probability of the generalised distribution defined by generalised polylog- arithm, Punjab University, Journal of Mathematics, Vol 51(7) (2019), 19-26.
  • [16] S. Owa, On certain classes of univalent functions in the unit disc, Kyungpook Math. J., Vol. 24, No. 2 (1984), 127-136.
  • [17] K.S. Padmanabhan, On certain classes of starlike functions in the unit disc, J. Indian Math. Soc. 32(1968), 89-103.
  • [18] S. Porwal, An application of a Poisson distribution series on certain analytic functions, J. Complex Anal., (2014), Art. ID 984135, 1–3.
  • [19] H. Silverman, Starlike and convexity properties for hypergeometric functions, J. Math. Anal. Appl. 172 (1993), 574–581.
  • [20] H. M. Srivastava, G. Murugusundaramoorthy and S. Sivasubramanian, Hypergeometric functions in the parabolic starlike and uniformly convex domains, Integr. Transf. Spec. Func. 18 (2007), 511–520.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Basem Frasin 0000-0001-8608-8063

Publication Date June 30, 2020
Published in Issue Year 2020

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