Document Type : Research Paper
Authors
Department of Mathematics, Faculty of Science, Dicle University, Diyarbakir, Turkiye.
Abstract
The aim of this article is to obtain some necessary and sufficient conditions for functions, whose coefficients are probabilities of the Miller-Ross-type Poisson distribution series, to belong to certain subclasses of analytic and univalent functions. Furthermore, we consider an integral operator related to the Miller-Ross type Poisson distribution series.
Keywords
[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(4), (2015), pp.2989-2992.
[2] S. Altinkaya and S. Yalcin Poisson Distribution Series for Analytic Univalent Functions, Complex Anal. Oper. Theory, 12, (2018), pp. 1315-1319.
[3] O. Altintas, A subclass of analytic functions with negative coefficients, Bull. Sci. Eng. Hacet. Univ., 19, (1990), pp. 15-24.
[4] O. Altintas and S. Owa, On a subclass of certain starlike functions with negative coefficients, Pusan Kyongnam Math. J., 4(3), (1988), pp. 41-56.
[5] 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), pp. 1023-1034.
[6] D. Bajpai, A study of univalent functions associated with distortion series and q-calculus, M.Phil., dissertation, CSJM Univerity, Kanpur, India (2016).
[7] T. Bulboaca and G. Murugusundaramoorthy, Univalent functions with positive coefficients involving Pascal distribution series, Commun. Korean Math. Soc., 35(3), (2020), pp. 867-877.
[8] PL Duren, Univalent Functions, Grundlehren der mathematischen Wissenschaften 259, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.
[9] S.M. El-Deeb, T. Bulboaca and J. Dziok , Pascal Distribution Series Connected with Certain Subclasses of Univalent Functions, Kyungpook Math. J., 59(2), (2019), pp. 301-314.
[10] 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(1), (2021), pp. 99-110.
[11] 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(3), (2021), pp. 147-154.
[12] 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).
[13] 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.
[14] G. Murugusundaramoorthy and S. Yalcin, Uniformly starlike functions and uniformly convex functions related to the Pascal distribution, Math. Bohem., 146(4) (2021), pp. 419-428.
[15] 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.,(2021).
[16] 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(1) (2019), pp. 11-17.
[17] A.T. Oladipo, Analytic Univalent Functions Defined by Generalized Discrete Probability Distribution, Earthline J. Math. Sci., 5(1), (2021), pp. 169-178.
[18] S. Porwal, An application of a Poisson distribution series on certain analytic functions, J. Complex Anal., (2014), pp. 1-3 , Article ID 984135.
[19] S. Porwal and M. Kumar, A unified study on starlike and convex functions associated with Poisson distribution series, Afr. Math., 27(5-6) (2016), pp. 1021-1027.
[20] S. Porwal and K.K. Dixit, On Mittag–Leffler type Poisson distribution, Afr. Math., 28(1-2), (2017), pp. 29-34.
[21] S. Porwal, Generalized distribution and its geometric properties associated with univalent functions, J. Complex Anal., (2018), pp. 1-5.
[22] 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(3), (2020), pp. 1035-1043.
[23] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51 (1975), pp. 109-116.
[24] H.M. Srivastava and S.M. El-Deeb, Fuzzy Differential Subordinations Based upon the Mittag-Leffler Type Borel Distribution, Symmetry, 13(6), (2021), 1023.
[25] 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), pp. 103-118.
[26] 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, Surveys Math. Appl., 16, (2021), pp. 193-205.
[27] B. Seker and S. Sumer Eker, On certain subclasses of starlike and convex functions associated with Pascal distribution series, Turkish J. Math., 44(6), (2020), pp. 1982-1989.
[28] 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), pp. 849-857.
[29] A.K. Wanas and N.A.J. Al-Ziadi, Applications of Beta Negative Binomial Distribution Series on Holomorphic Functions, Earthline J. Math. Sci., 6(2) (2021), pp. 271-292.
)
