Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

SOME INCLUSION RELATIONS OF CERTAIN SUBCLASSES OF HARMONIC UNIVALENT FUNCTIONS ASSOCIATED WITH GENERALIZED DISTRIBUTION SERIES

  • Received : 2019.09.28
  • Accepted : 2020.03.26
  • Published : 2020.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of this present paper is to obtain inclusion relations between various subclasses of harmonic univalent functions by using the convolution operator associated with generalized distribution series. To be more precise, we obtain such inclusions with harmonic starlike and harmonic convex mappings in the plane.

Keywords

Acknowledgement

The authors would like to thank the referee for his insightful suggestions to improve the paper in current form.

References

  1. M. S. Ahmad, Q. Menmood, W. Nazeer, and A. U. Haq, An application of a hypergeometric distribution series on certain analytic functions, Sci. Gnt. 27 (2015), 2989-2992.
  2. O. P. Ahuja, Connections between various subclasses of planar harmonic mappings involving hypergeometric functions, Appl. Math. Comput. 198 (2008), no. 1, 305-316. https://doi.org/10.1016/j.amc.2007.08.035
  3. S. Altinkaya and S. Yalcin, Poisson distribution series for certain subclasses of starlike functions with negative coefficients, An. Univ. Oradea Fasc. Mat. 24 (2017), no. 2, 5-8.
  4. S. Altinkaya and S. Yalcin, Poisson distribution series for analytic univalent functions, Complex Anal. Oper. Theory 12 (2018), no. 5, 1315-1319. https://doi.org/10.1007/s11785-018-0764-y
  5. A. Baricz, Generalized Bessel functions of the first kind, Lecture Notes in Mathematics, 1994, Springer-Verlag, Berlin, 2010. https://doi.org/10.1007/978-3-642-12230-9
  6. V. B. L. Chaurasia and H. S. Parihar, Certain sufficiency conditions on Fox-Wright functions, Demonstratio Math. 41 (2008), no. 4, 813-822. https://doi.org/10.1515/dema-2008-0409
  7. J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 9 (1984), 3-25. https://doi.org/10.5186/aasfm.1984.0905
  8. P. Duren, Harmonic mappings in the plane, Cambridge Tracts in Mathematics, 156, Cambridge University Press, Cambridge, 2004. https://doi.org/10.1017/CBO9780511546600
  9. J. M. Jahangiri, Harmonic functions starlike in the unit disk, J. Math. Anal. Appl. 235 (1999), no. 2, 470-477. https://doi.org/10.1006/jmaa.1999.6377
  10. N. Magesh, S. Porwal, and C. Abirami, Starlike and convex properties for Poisson distribution series, Stud. Univ. Babes-Bolyai Math. 63 (2018), no. 1, 71-78. https://doi.org/10.24193/subbmath.2018.1.05
  11. G. Murugusundaramoorthy, K. Vijaya, and S. Porwal, Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series, Hacet. J. Math. Stat. 45 (2016), no. 4, 1101-1107.
  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 (2019), no. 1, 11-17.
  13. S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 (1987), no. 5, 1057-1077. https://doi.org/10.4153/CJM-1987-054-3
  14. S. Ponnusamy and M. Vuorinen, Univalence and convexity properties for Gaussian hypergeometric functions, Rocky Mountain J. Math. 31 (2001), no. 1, 327-353. https://doi.org/10.1216/rmjm/1008959684
  15. S. Porwal, An application of a Poisson distribution series on certain analytic functions, J. Complex Anal. 2014 (2014), Art. ID 984135, 3 pp. https://doi.org/10.1155/2014/984135
  16. S. Porwal, Generalized distribution and its geometric properties associated with univalent functions, J. Complex Anal. 2018 (2018), Art. ID 8654506, 5 pp. https://doi.org/10.1155/2018/8654506
  17. S. Porwal, S. Altinkaya, and S. Yalcin, The Poisson distribution series of general subclasses of univalent functions, Acta Univ. Apulensis Math. Inform. No. 58 (2019), 45-52. https://doi.org/10.17114/j.aua.2019.58.04
  18. S. Porwal and K. K. Dixit, An application of hypergeometric functions on harmonic univalent functions, Bull. Math. Anal. Appl. 2 (2010), no. 4, 97-105.
  19. S. Porwal and M. Kumar, A unified study on starlike and convex functions associated with Poisson distribution series, Afr. Mat. 27 (2016), no. 5-6, 1021-1027. https://doi.org/10.1007/s13370-016-0398-z
  20. S. Porwal and M. Kumar, Confluent hypergeometric distribution and its applications on certain classes of univalent functions, Afr. Mat. 28 (2017), no. 1-2, 1-8. https://doi.org/10.1007/s13370-016-0422-3
  21. S. Porwal, N. Magesh, and V. K. Balaji, On certain subclasses of analytic functions associated with confluent hypergeometric distribution, Southeast Asian Bull. Math. 43 (2019), no. 4, 577-584.
  22. S. Porwal, N. Magesh, and C. Murugesan, On certain classes of analytic functions involving Poisson distribution series, An. Univ. Oradea Fasc. Mat. 24 (2017), no. 2, 15-22.
  23. R. K. Raina and P. Sharma, Harmonic univalent functions associated with Wright's generalized hypergeometric functions, Integral Transforms Spec. Funct. 22 (2011), no. 8, 561-572. https://doi.org/10.1080/10652469.2010.535797
  24. H. Silverman and E. M. Silvia, Subclasses of harmonic univalent functions, New Zealand J. Math. 28 (1999), no. 2, 275-284.