A Certain Families of Bi-Univalent Functions with Respect to Symmetric Conjugate Points Defined by Beta Negative Binomial Distribution Series
DOI:
https://doi.org/10.29304/jqcm.2023.15.2.1252Keywords:
: Analytic functions, Bi-univalent functions, Symmetric conjugate points,, Coefficient estimates, Beta negative binomial distribution.Abstract
The objective of this paper is to introduce and investigate two families of analytical and bi-univalent functions, and , with respect to symmetric conjugate points that are defined in the open unit disk and connected to a series of beta-negative binomial distributions. For functions in each of these families, we look into upper bounds for the initial Taylor-Maclaurin coefficients and .
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References
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[14] H. M. Srivastava , A . Motamednezhad and E. A . Adegani, Faber polynomial Coefficient estimates for bi-univalent functions defined by using differential subordination and a certain fractional derivative operator, Mathematics, 8 (2020), Art. ID 172, 1-12.
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[19] A. K. Wanas and N. A. Al-Ziadi, Applications of Beta negative binomial distribution series on holomorphic functions, Earthline J. Math. Sci., 6(2) (2021), 271-292.
[20] A. K. Wanas and J. A. Khuttar, Applications of Borel distribution series on analytic functions, Earthline J. Math. Sci., 4(1) (2020), 71-82.
[2] S. Altlnkaya and S. Yalcin, Poisson distribution series for certain subclasses of starlike functions with negative coefficients, An. Univ. Oradea Fasc. Mat., 24(2) (2017), 5-8.
[3] P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer –Verlag, New York, Berlin, Heideiberg and Tokyo, 1983.
[4] 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), 301-314.
[5] D. Guo , E. Ao, H. Tang and L. P. Xiong, Initial bounds for a subclass of analytic and bi-univalent functions defined by Chebyshev polynomials and q-differential operator, J. Math. Research Appl., 39(5) (2019), 506-516.
[6] Y .Li, K .Vijaya, G. Murugusundaramoorthy and H. Tang, On new subclasses of bi-starlike functions with bounded boundary rotation, AIMS Mathematics, 5(4) (2020), 3346-3356.
[7] W. Naszeer, 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), 11-17.
[8] A. O. Pall-Szabo and A. K. Wanas, Coefficient estimates for some new classes of bi- Bazilevic functions of Ma-Minda type involving the salagean integro- differential operator, Quasestiones Mathematicae, 44(4) (2021), 495-502.
[9] S. Porwal and M. Kumar, A unified study on starlike and convex functions associated with Poisson distribution series, Afr. Mat., 27 (2016), 10-21.
[10] B. Seker, On a new subclass of bi-univalent functions defined by using Salagean operator, Turk. J. Math., 42 (2018), 2891-2896.
[11] T. G . Shaba, On some subclasses of bi-pseudo-starlike functions defined by Salsgean differential operator, Asia Pac. J. Math., 8(6) (2021), 1-11.
[12] H. M. Srivastava, S. S. Eker, S . G. Hamidi and J. M. Jahangiri, Faber polynomial coefficient estimates for bi-univalent functions defined by the Tremblay fractional derivative operator, Bull. Iran. Math. Soc., 44 (2018) , 149-157.
[13] H. M . Srivastava, A. K . Mishra and P . Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23 (2010), 1188-1192.
[14] H. M. Srivastava , A . Motamednezhad and E. A . Adegani, Faber polynomial Coefficient estimates for bi-univalent functions defined by using differential subordination and a certain fractional derivative operator, Mathematics, 8 (2020), Art. ID 172, 1-12.
[15] H. M. Srivastava, F. M. Sakar and H. O. Guney , Some general coefficient estimates for a new class of analytic and bi- univalent functions defined by a linear combination , Filomat, 32 (2018), 1313-1322.
[16] S. R .Swamy, P . K. Mamatha, N. Magesh and J .Yamini, Certain subclasses of bi-univalent functions defined by Salagean operator associated with the (p,q) – Lucas polynomials, Advances in Mathematics Scientific Journal, 9(8) (2020), 6017-6025.
[17] H. Tang, N. Magesh, V. K. Balaji and C. Abirami, Coefficient inequalities for comprehensive class of bi-univalent functions related with bounded boundary variation, J. Ineq. Appl., 2019 (2019), Art. ID 237, 1-9.
[18] A. K. Wanas and A. K. Al-Khafaji, Coefficient bounds for certain families of bi-univalent
functions defined by Wanas operator, Asian-Eur. J. Math., 15(5) (2022), 1-9.
[19] A. K. Wanas and N. A. Al-Ziadi, Applications of Beta negative binomial distribution series on holomorphic functions, Earthline J. Math. Sci., 6(2) (2021), 271-292.
[20] A. K. Wanas and J. A. Khuttar, Applications of Borel distribution series on analytic functions, Earthline J. Math. Sci., 4(1) (2020), 71-82.
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Published
2023-09-25
How to Cite
Wanas, A. K., & Khudher, F. C. (2023). A Certain Families of Bi-Univalent Functions with Respect to Symmetric Conjugate Points Defined by Beta Negative Binomial Distribution Series. Journal of Al-Qadisiyah for Computer Science and Mathematics, 15(2), Math Page 102–110. https://doi.org/10.29304/jqcm.2023.15.2.1252
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Math Articles
