Necessary and sufficient conditions for functions defined by binomial distribution to be in a general class of analytic functions
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Abstract
In this paper, a comprehensive class ΘΨ(El, E2, E3) of univalent functions is examined in light of the recent findings on binomial distribution. Additionally, we provide some requirements for the functions B(λ, γ, ς), B(λ, π, ς)b and the operator L(λ, γ, ς) defined by the binomial distribution to be in these subclasses. This study will motivate the authors to discover new sufficient requirements, not only for binomial distributions but also for numerous other special functions. Additionally, we summarize many previous studies.
References
O. Altintas and S. Owa, On subclasses of univalent functions with negative coefficients, Pusan Kyongnam Math.J., 4(1988), 41–46.
O. Altintas, O. Oskan and H. M. Srivastava, Neighborhoods of a class of analytic functions with negative coefficients, Appl. Math. Lett., 13, (2000), 63–67.
R. M. El-Ashwah and W. Y Kota, Some condition on a Poisson distribution series to be in subclasses of univalent functions, Acta Univ. Apulensis Math. Inform., 51, (2017), 89–103.
R. Bharati, R. Parvatham and A. Swaminathan, On subclasses of uniformly convex functions and corresponding class of starlike functions, Tamkang J. Math., 26, (1997), 17–32.
S. M. El-Deeb, T. BulboacaV and J. Dziok, Pascal distribution series connected with certain subclasses of univalent functions, Kyungpook Math. J., 59, (2019), 301–314.
B.A. Frasin, F. Yousef, T. Al-Hawary and I. Aldawish, Application of generalized Bessel functions to classes of analytic functions, Afr. Mat., 32, (2021), 431–439.
B.A. Frasin, On certain subclasses of analytic functions associated with Poisson distribution series, Acta Univ.Sapientiae, Mathematica, 11(1), (2019) 78–86.
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, (2019), 223–230.
V. P. Gupta and P. K. Jain, Certain classes of univalent functions with negative coefficients, Bull. Aust.Math. Soc.,14 (1976), 409–416.
T. Al-Hawary, B. A. Frasin and A. Amourah, Results and inclusion properties for binomial distribution, Palestine J.Math., in press.
T. Al-Hawary, I. Aldawish, B. A. Frasin, O. Alkam and F. Yousef, Necessary and sufficient conditions for normalized Wright functions to be in certain classes of analytic functions, Mathematics, 10(24), (2022), Ar. 4693, 1–11.
T. Al-Hawary, B. A. Frasin and I. Aldawish, Applications of generalized hypergeometric distribution on comprehensive families of analytic functions, Symmetry, 16, (2024), Ar. 982, 1–13.
T. Janani and G. Murugusundaramoorthy, Inclusion results on subclasses of starlike and convex functions associated with Struve functions, Italian J. Pure Applied Math., 32, (2014), 467–476.
G. Murugusundaramoorthy, K. Vijaya, and K. Uma, Subordination results for a class of analytic functions involving the Hurwitz-Lerch zeta function, Int. J. Nonlinear Sci. , 10(4), (2010), 430–437.
G. Murugusundaramoorthy, B. A. Frasin and Tariq Al-Hawary, Uniformly convex spiral functions and uniformly spirallike function associated with Pascal distribution series, Mat. Bohem., 23, (2021), 1–11.
W. Nazeer, Q, Mehmood, S. M. Kang, and A. Ul Haq, An application of binomial distribution series on certain analytic functions, J. Comput Anal Appl., 26(1), (2019), 11–17.
C. Selvaraj and R. Geetha, On subclasses of uniformly convex spirallike functions and corresponding class of spiral like functions, Int. J. Contemp. Math. Sci., 5(37), (2010), 1845–1854.
A. Swaminathan, Certain sufficient conditions on Gaussian hypergeometric functions, J. Inequal. Pure Applied Math., 4(5), (2004), Art. 83, 1–10, 2004.
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