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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science
Full Length Article

Volume 25 • Issue 1 • PP: 228-238 • 2024

Collection of Bi-Univalent Functions Using Bell Distribution Associated With Jacobi Polynomials

Ala Amourah 1*
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,
Tariq Al-Hawary 2
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,
Feras Yousef 3
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,
Jamal Salah 4
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1Mathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 3111, Oman; Jadara Research Center, Jadara University, Irbid 21110, Jordan.
2Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816. Jordan; Jadara Research Center, Jadara University, Irbid 21110, Jordan.
3Department of Mathematics, The University of Jordan, Amman 11942, Jordan; Jadara Research Center, Jadara University, Irbid 21110, Jordan
4College of Applied and Health Sciences, A’Sharqiyah University, Post Box No. 42, Post Code No. 400 Ibra, Sultanate of Oman
* Corresponding Author.
DOI https://doi.org/10.54216/IJNS.250121
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Received: December 18, 2023 Revised: February 05, 2024 Accepted: June 26, 2024
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Abstract

The aim of this study is to present novel collections of bi-univalent functions, which are characterized using the Bell Distribution. These collections are delineated through the application of Jacobi polynomials. We have established bounds for the Taylor-Maclaurin coefficients, particularly |a2| and |a3|. Additionally, we have investigated the Fekete-Szeg¨o functional issues pertinent to functions within these subclasses. By concentrating on particular parameters in our principal findings, we have identified numerous new insights.

 

Keywords

Jacobi polynomials analytic functions univalent functions bi-univalent functions Fekete-Szeg&uml o problem. &nbsp

References

[1] A. Legendre, Recherches sur laattraction des sph´eroides homog´enes, M´emoires pr´esentes par divers savants a laAcad´emie des Sciences de laInstitut de France, Paris, 10 (1785), 411-434.

[2] H. Bateman, Higher Transcendental Functions. McGraw-Hill, 1953.

[3] P.L. Duren, Univalent Functions. Grundlehren der MathematischenWissenschaften, Band 259, Springer- Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.

[4] S. S. Miller, P. T. Mocanu, Second Order Differential Inequalities in the Complex Plane. J. Math. Anal. Appl. 65 (1978), 289–305.

[5] S. S. Miller, P. T. Mocanu, Differential Subordinations and Univalent Functions. Mich. Math. J. 28 (1981), 157–172.

[6] S. S. Miller, P. T. Mocanu, Differential Subordinations. Theory and Applications. Marcel Dekker, Inc.: New York, NY, USA, 2000.

[7] S. Bulut, Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad Journal of Mathematics 43 (2013), 59–65.

[8] B.A. Frasin, Coefficient bounds for certain classes of bi-univalent functions, Hacettepe Journal of Mathematics and Statistics 43.3 (2014), 383-389.

[9] B. A. Frasin, M. K. Aouf, New subclasses of bi-univalent functions, Applied Mathematics Letters 24 (2011), 1569–1573.

[10] Tariq Al-Hawary, Ala Amourah, Abdullah Alsoboh, and Omar Alsalhi. A new comprehensive subclass of analytic bi-univalent functions related to gegenbauer polynomials. Symmetry 15.3 (2023): 576.

[11] G. Murugusundaramoorthy, N. Magesh, V. Prameela, Coefficient bounds for certain subclasses of biunivalent function, Abstract and Applied Analysis, Volume 2013, Article ID 573017, 3 pages.

[12] Z. Peng,G. Murugusundaramoorthy, T. Janani, Coefficient estimate of bi-univalent functions of complex order associated with the Hohlov operator, Journal of Complex Analysis, Volume 2014, Article ID 693908, 6 pages.

[13] A. A. Amourah and Feras Yousef. Some properties of a class of analytic functions involving a new generalized differential operator. Boletim da Sociedade Paranaense de Matematica 38.6 (2020), 33-42.

[14] F. Yousef, B.A. Frasin, T. Al-Hawary, Fekete-Szeg¨o inequality for analytic and bi-univalent functions subordinate to Chebyshev polynomials. Filomat 32.9 (2018), 3229-3236.

[15] F. Yousef, T. Al-Hawary, G. Murugusundaramoorthy, Fekete-Szeg¨o functional problems for some subclasses of bi-univalent functions defined by Frasin differential operator. Afrika Matematika 30.3-4 (2019), 495–503.

[16] F. Yousef, S. Alroud, M. Illafe, New subclasses of analytic and bi-univalent functions endowed with coefficient estimate problems. Analysis and Mathematical Physics 11. 2 (2021), 1-12.

[17] F. Yousef, A. Amourah, B.A. Frasin, T. Bulboac, An avant-Garde construction for subclasses of analytic bi-univalent functions. Axioms 11.6 (2022), 267.

[18] Abdullah Alsoboh, Muratlar, and Mucahit Buyankara. Fekete-Szeg¨o Inequality for a Subclass of Bi- Univalent Functions Linked to q-Ultraspherical Polynomials. Contemporary Mathematics (2024), 2366- 2380.

[19] Abdullah Alsoboh and Georgia Irina Oros. A Class of Bi-Univalent Functions in a Leaf-Like Domain Defined through Subordination via q -Calculus. Mathematics 12.10 (2024), 1594.

[20] F. Castellares, S. L. Ferrari, A. J. Lemonte, On the Bell distribution and its associated regression model for count data, Applied Mathematical Modelling 56 (2018), 172-185.

[21] E. T. Bell, Exponential polynomials, Annals of Mathematics 35 (1934),258-277 .

[22] E. T. Bell, Exponential numbers, The American Mathematical Monthly 41.7 (1934), 411-419.

[23] M. Marcokova, V. Guldan, Jacobi Polynomials and Some Related Functions. In Mathematical Methods in Engineering (pp. 219-227). Springer Netherlands.

[24] A. A. Amourah and Mohamed Illafe. A Comprehensive Subclass of Analytic and Bi-Univalent Functions Associated with Subordination.Palestine Journal of Mathematics 9.1 (2020).

[25] A. Amourah, T. Al-Hawary, B. A. Frasin, Application of Chebyshev polynomials to certain class of bi- Bazileviˇc functions of order α + iβ. Afrika Matematika 32 .5 (2021), 1059-1066.

[26] A. Amourah, M. Alomari, F. Yousef, A. Alsoboh, Consolidation of a Certain Discrete Probability Distribution with a Subclass of Bi-Univalent Functions Involving Gegenbauer Polynomials. Mathematical Problems in Engineering 2022 (2022).

[27] A. Amourah, B. A. Frasin, M. Ahmad, F. Yousef, Exploiting the Pascal distribution series and Gegenbauer polynomials to construct and study a new subclass of analytic bi-univalent functions. Symmetry 14.1 (2022), 147.

[28] T. Al-Hawary, A. Amourah, B. A. Frasin, Fekete-Szeg¨o inequality for bi-univalent functions by means of Horadam polynomials. Boletin de la Sociedad Matematica Mexicana 27. 3 (2021), 1-12.

[29] M. Illafe, A. Amourah, M. Haji Mohd, Coefficient estimates and FeketeˆaC“Szeg?¶ functional inequalities for a certain subclass of analytic and bi-univalent functions. Axioms 11.4 (2022), 147.

[30] A. Hussen, M. Illafe, Coefficient Bounds for a Certain Subclass of Bi-Univalent Functions Associated with Lucas-Balancing Polynomials. Mathematics 11.24 (2023), 4941.

[31] A. Hussen, A. Zeyani, Coefficients and FeketeˆaC“Szeg¨o Functional Estimations of Bi-Univalent Subclasses Based on Gegenbauer Polynomials. Mathematics 11.13 (2023), 2852.

[32] A. Hussen, An Application of the Mittag-Leffler-type Borel Distribution and Gegenbauer Polynomials on a Certain Subclass of Bi-Univalent Functions. Heliyon 9 (2024), e31469.

[33] A. Hussen, M. S. Madi, A. M. Abominjil, Bounding coefficients for certain subclasses of bi-univalent functions related to Lucas-Balancing polynomials. AIMS Mathematics 9.7 (2024), e31469.

[34] M. Illafe, F. Yousef, M. Haji Mohd, S. Supramaniam, Initial Coefficients Estimates and Fekete-Szeg¨o Inequality Problem for a General Subclass of Bi-Univalent Functions Defined by Subordination. Axioms 12.3 (2023), 235.

[35] B. A. Frasin, T. Al-Hawary, F. Yousef, I. Aldawish, On subclasses of analytic functions associated with Struve functions. Nonlinear Functional Analysis and Applications 27.1 (2022), 99-110.

[36] A. Amourah, N. Anakira, M. J. Mohammed and M. Jasim, Jacobi polynomials and bi-univalent functions. Computer Science, 19(4) (2024), 957-968.

[37] A. Amourah, A. Alsoboh, D. Breaz and S. M. El-Deeb, A Bi-Starlike Class in a Leaf-like Domain Defined through Subordination via q- Calculus. Mathematics, 12(11) (2024), 1735.

[38] A. Amourah, B. A. Frasin, J. Salah and T. Al-Hawary, Fibonacci Numbers Related to Some Subclasses of Bi-Univalent Functions. International Journal of Mathematics and Mathematical Sciences, 2024(1) (2024), 8169496.

[39] M. Fekete, G. Szego¨, Eine Bemerkung A˜ber ungerade schlichte Funktionen. Journal of the LondonMathematical Society 1.2 (1933), 85-89.

 

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format_quote
Amourah, Ala, Al-Hawary, Tariq, Yousef, Feras, Salah, Jamal. "Collection of Bi-Univalent Functions Using Bell Distribution Associated With Jacobi Polynomials." International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 1, 2024, pp. 228-238. DOI: https://doi.org/10.54216/IJNS.250121
Amourah, A., Al-Hawary, T., Yousef, F., Salah, J. (2024). Collection of Bi-Univalent Functions Using Bell Distribution Associated With Jacobi Polynomials. International Journal of Neutrosophic Science, Volume 25(Issue 1), 228-238. DOI: https://doi.org/10.54216/IJNS.250121
Amourah, Ala, Al-Hawary, Tariq, Yousef, Feras, Salah, Jamal. "Collection of Bi-Univalent Functions Using Bell Distribution Associated With Jacobi Polynomials." International Journal of Neutrosophic Science Volume 25, no. Issue 1 (2024): 228-238. DOI: https://doi.org/10.54216/IJNS.250121
Amourah, A., Al-Hawary, T., Yousef, F., Salah, J. (2024) 'Collection of Bi-Univalent Functions Using Bell Distribution Associated With Jacobi Polynomials', International Journal of Neutrosophic Science, Volume 25(Issue 1), pp. 228-238. DOI: https://doi.org/10.54216/IJNS.250121
Amourah A, Al-Hawary T, Yousef F, Salah J. Collection of Bi-Univalent Functions Using Bell Distribution Associated With Jacobi Polynomials. International Journal of Neutrosophic Science. 2024;Volume 25(Issue 1):228-238. DOI: https://doi.org/10.54216/IJNS.250121
A. Amourah, T. Al-Hawary, F. Yousef, J. Salah, "Collection of Bi-Univalent Functions Using Bell Distribution Associated With Jacobi Polynomials," International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 1, pp. 228-238, 2024. DOI: https://doi.org/10.54216/IJNS.250121
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