Article ID: MTJPAM-D-21-00008

Title: Mapping properties of generalized distribution series on univalent functions

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

Article ID: MTJPAM-D-21-00008; Volume 4 / Issue 1 / Year 2022, Pages 31-36

Document Type: Research Paper

Author(s): Saurabh Porwal a , Nanjundan Magesh b , Rajavadivelu Themangani c

aDepartment of Mathematics R. S. Government Degree College, Bairi-Shivrajpur-Kanpur-209205, (U.P.), India

bPost-Graduate and Research Department of Mathematics Govt Arts College (Men), Krishnagiri – 635 001, Tamilnadu, India

cDepartment of Mathematics Voorhees College, Vellore – 632 001, Tamilnadu, India

Received: 4 January 2021, Accepted: 3 September 2021, Published: 25 September 2021.

Corresponding Author: Saurabh Porwal (Email address:

Full Text: PDF


In this work, the generalized distribution series which is constructed by probability mass function is considered to discuss certain properties of classes of univalent functions. Moreover, we discuss certain connections between different subclasses of univalent functions.

Keywords: Analytic functions, univalent functions, convex functions, starlike functions, generalized distribution series, probability mass function

  1. M. S. Ahmad, Q. Menmood, W. Nazeer and A. U. Haq, An application of a hypergeometric distribution series on certain analytic functions, Sci. Int. 27, 2989–2992, 2015.
  2. S. Altinkaya and S. Yalçin, Poisson distribution series for analytic univalent functions, Complex Anal. Oper. Theory 12 (5), 1315–1319, 2018.
  3. A. Baricz, Generalized Bessel functions of the first kind, Lecture Notes in Mathematics (1994), Springer-Verlag, Berlin, 2010.
  4. V. B. L. Chaurasia and H. S. Parihar, Certain sufficiency conditions on Fox-Wright functions, Demonstratio Math. 41 (4), 813–822, 2008.
  5. K. K. Dixit and V. Chandra, On subclass of univalent functions with positive coefficients, Aligarh Bull. Math. 27 (2), 87–93, 2008.
  6. K. K. Dixit and A. L. Pathak, A new class of analytic functions with positive coefficients, Indian J. Pure Appl. Math. 34 (2), 209–218, 2003.
  7. K. K. Dixit and S. K. Pal, On a class of univalent functions related to complex order, Indian J. Pure Appl. Math. 26, 889–896, 1995.
  8. K. K. Dixit, S. Porwal and A. Dixit, A new subclass of univalent functions with positive coefficients, Bessel J. Math. 3 (2), 125–135, 2013.
  9. B. A. Frasin, T. Al-Hawary and F. Yousef, Necessary and sufficient conditions for hypergeometric functions to be in a subclass of analytic functions, Afr. Mat. 30 (1-2), 223–230, 2019.
  10. B. A. Frasin, F. Yousef, T. Al-Hawary and I. Aldawish, Application of generalized Bessel functions to classes of analytic functions, Afr. Mat. 32 (3-4), 431–439, 2021.
  11. N. Magesh, S. Porwal and C. Abirami, Starlike and convex properties for Poisson distribution series, Stud. Univ. Babeş-Bolyai Math. 63 (1), 71–78, 2018.
  12. W. Nazeer, Q. Mehmood, S. M. Kang and A. U. Haq, An application of Binomial distribution series on certain analytic functions, J.Comput. Anal. Appl. 26, 11–17, 2019.
  13. S. Ponnusamy and F. Rønning, Starlikeness properties for convolutions involving hypergeometric series, Ann. Univ. Mariae Curie-Skłodowska Sect. A 52 (1), 141–155, 1998.
  14. S. Porwal, An application of a Poisson distribution series on certain analytic functions, J. Complex Anal. 2014, Art. ID 984135, 3 pp.
  15. S. Porwal, An application of certain convolution operator involving Poisson distribution series, Asian-Eur. J. Math. 9 (4), 1650085, 8 pp, 2016.
  16. S. Porwal, Generalized distribution and its geometric properties associated with univalent functions, J. Complex Anal. 2018, Art. ID 8654506, 5 pp, 2018.
  17. S. Porwal and M. Ahmad, Some sufficient conditions for generalized Bessel functions associated with conic regions, Vietnam J. Math. 43 (1), 163–172, 2015.
  18. S. Porwal and K. K. Dixit, An application of certain convolution operator involving hypergeometric functions, J. Rajasthan Acad. Phys. Sci. 9 (2), 173–186, 2010.
  19. S. Porwal and S. Kumar, Confluent hypergeometric distribution and its applications on certain classes of univalent functions, Afr. Mat. 28 (1-2), 1–8, 2017.
  20. S. Porwal, K.K. Dixit, Vinod Kumar and P. Dixit, On a subclass of analytic function defined by convolution, Gen. Math. 19 (3), 57–65, 2011.
  21. R. K. Raina, On univalent and starlike Wright’s hypergeometric functions, Rend. Sem. Mat. Univ. Padova 95, 11–22, 1996.
  22. H. M. Srivastava, G. Murugusundaramoorthy and S. Sivasubramanian, Hypergeometric functions in the parabolic starlike and uniformly convex domains, Integral Transforms Spec. Funct. 18 (7-8), 511–520, 2007.
  23. A. Swaminathan, Certain sufficiency conditions on Gaussian hypergeometric functions, J. Inequal. Pure Appl. Math. 5 (4), Article 83, 10 pp, 2004.
  24. B. A. Uralegaddi, M. D. Ganigi and S. M. Sarangi, Univalent functions with positive coefficients, Tamkang J. Math. 25 (3), 225–230, 1994.
  25. B. A. Uralegaddi, M. D. Ganigi and S. M. Sarangi, Close-to-convex functions with positive coefficients, Studia Univ. Babeş-Bolyai Math. 40 (4), 25–31, 1995.