Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS ASSOCIATED WITH MILLER-ROSS-TYPE POISSON DISTRIBUTION SERIES

  • Bilal, SEKER (Department of Mathematics, Faculty of Science, Dicle University) ;
  • Sevtap, SUMER EKER (Department of Mathematics, Faculty of Science, Dicle University) ;
  • Bilal, CEKIC (Department of Mathematics, Faculty of Science, Dicle University)
  • Received : 2021.12.06
  • Accepted : 2022.07.28
  • Published : 2022.12.25
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of the present paper is to obtain some sufficient conditions for analytic functions, whose coefficients are probabilities of the Miller-Ross type-Poisson distribution series, to belong to classes 𝓖(λ, 𝛿) and 𝓚(λ, 𝛿).

Keywords

References

  1. M. S. Ahmad, Q. Mehmood, W. Nazeer, and A. U. Haq, An application of a Hypergeometric distribution series on certain analytic functions, Sci. Int.(Lahore) 27 (2015), no. 4, 2989-2992.
  2. S. Altinkaya and S. Yal,cin 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
  3. A. Altunhan and S. Sumer Eker, On certain subclasses of univalent functions of complex order associated with poisson distribution series, Bol. Soc. Mat. Mex. 26 (2020), no. 3, 1023-1034. https://doi.org/10.1007/s40590-020-00298-9
  4. D. Bajpai, A study of univalent functions associated with distortion series and qcalculus, M. Phil., Dissertation, CSJM Univerity, Kanpur, India, 2016.
  5. T. Bulboaca and G. Murugusundaramoorthy, Univalent functions with positive coefficients involving Pascal distribution series, Commun. Korean Math. Soc. 35 (2020), no. 3, 867-877. https://doi.org/10.4134/CKMS.C190413
  6. 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.
  7. PL Duren, Univalent Functions, Grundlehren der mathematischen Wissenschaften 259, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.
  8. S. M. El-Deeb, T. Bulboaca and J. Dziok , Pascal Distribution Series Connected with Certain Subclasses of Univalent Functions, Kyungpook Math. J. 59 (2019), no. 2, 301-314. https://doi.org/10.5666/KMJ.2019.59.2.301
  9. B. A. Frasin, S. R. Swamy, and A. K. Wanas, Subclasses of starlike and convex functions associated with Pascal distribution series, Kyungpook Math. J. 61 (2021), no. 1, 99-110. https://doi.org/10.5666/KMJ.2021.61.1.99
  10. B. A. Frasin, S. Porwal, and F. Yousef, Subclasses of Starlike and Convex Functions Associated with Mittag-Leffler-type Poisson Distribution Series, Montes Taurus J. Pure Appl. Math. 3 (2021), no. 3, 147-154.
  11. K. S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, John Wiley and Sons, New York, Chichester, Brisbane, Toronto and Singapore, 1993.
  12. G. Murugusundaramoorthy and S. M. El-Deeb, Second Hankel determinant for a class of analytic functions of the Mittag-Leffler-type Borel distribution related with Legendre polynomials, Turkish World Math. Soc. J. Appl. Engineering Math. 14 (2022), no. 4, 1247-1258.
  13. 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.
  14. A. T. Oladipo, Analytic Univalent Functions Defined by Generalized Discrete Probability Distribution, Earthline Journal of Mathematical Sciences 5 (2021), no. 1, 169-178.
  15. S. Porwal, An application of a Poisson distribution series on certain analytic functions, J. Complex Anal. 2014 (2014), Art. ID 984135.
  16. 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
  17. S. Porwal and K. K. Dixit, On Mittag-Leffler type Poisson distribution, Afr. Mat. 28 (2017), no. 1-2, 29-34. https://doi.org/10.1007/s13370-016-0427-y
  18. S. Porwal, Generalized distribution and its geometric properties associated with univalent functions, J. Complex Anal. 2018 (2018), Art. ID 8654506.
  19. S. Porwal, N. Magesh, and C. Abirami, Certain subclasses of analytic functions associated with Mittag-Leffler-type Poisson distribution series, Bol. Soc. Mat. Mex. 26 (2020), no. 3, 1035-1043. https://doi.org/10.1007/s40590-020-00288-x
  20. B. Seker and S. Sumer Eker, On certain subclasses of starlike and convex functions associated with Pascal distribution series, Turkish J. Math. 44 (2020), no. 6, 1982-1989. https://doi.org/10.3906/mat-2003-12
  21. B. Seker and S. Sumer Eker, On certain subclass of univalent functions of complex order associated with Pascal distribution series, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 70 (2021), 849-857. https://doi.org/10.31801/cfsuasmas.844259
  22. B. Seker, S. Sumer Eker, and B. Cekic, On subclasses of analytic functions associated with Miller-Ross-type Poisson distribution series, Sahand Communications in Mathematical Analysis (SCMA), in press.
  23. H. M. Srivastava, A. K. Wanas, and G. Murugusundaramoorthy, A certain family of bi-univalent functions associated with the Pascal distribution series based upon the Horadam polynomials, Surv. Math. Appl. 16 (2021), 193-205.
  24. H. M. Srivastava, G. Murugusundaramoorthy, and S. M. El-Deeb Faber polynomial coefficient estimates of bi-close-to-convex functions connected with the Borel distribution of the Mittag-Leffler type, J. Nonlinear Var. Anal. 5 (2021), 103-118. https://doi.org/10.23952/jnva.5.2021.1.07
  25. H. M. Srivastava and S. M. El-Deeb, Fuzzy Differential Subordinations Based upon the Mittag-Leffler Type Borel Distribution, Symmetry 13 (2021), no. 6, 1023.
  26. H. M. Srivastava, B. Seker, S. Sumer Eker, and B. Cekic, A Class of Poisson Distributions Based upon a two parameter Mittag-Leffler type function, submitted.
  27. T. Thulasiram, K. Suchithra, T. V. Sudharsan, and G. Murugusundaramoorthy, Some inclusion results associated with certain subclass of analytic functions inolving Hohlov operator, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 108 (2014), no. 2, 711-720. https://doi.org/10.1007/s13398-013-0135-5
  28. A. K. Wanas and N. A. J. Al-Ziadi, Applications of Beta Negative Binomial Distribution Series on Holomorphic Functions, Earthline J. Math. Sci. 6 (2021), no. 2, 271-292.