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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 24 , Issue 4 , PP: 315-323, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

Two Inclusive Subfamilies of bi-univalent Functions

Tariq Al-Hawary 1 * , Ala Amourah 2 , Jamal Salah 3 , Feras Yousef 4

  • 1 Department of Applied Science, Ajloun College, Al Balqa Applied University, Ajloun 26816. Jordan. Jadara University Research Center, Jadara University, Jordan. - (tariq amh@bau.edu.jo)
  • 2 Mathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 3111, Oman. Jadara University Research Center, Jadara University, Jordan. - (alaammour@yahoo.com)
  • 3 College of Applied and Health Sciences, A’Sharqiyah University, Post Box No. 42, Post Code No. 400 Ibra, Sultanate of Oman. - (damous73@yahoo.com)
  • 4 Department of Mathematics, The University of Jordan, Amman 11942, Jordan. School of Engineering, Math & Technology, Navajo Technical University, Crownpoint, NM 87313, USA. Jadara University Research Center, Jadara University, Jordan. - (fyousef@ju.edu.jo)

    • Doi: https://doi.org/10.54216/IJNS.240422

    Received: September 18, 2023 Revised: February 15, 2024 Accepted: June 09, 2024
    Abstract

    The aim of this article is to establish two new and qualitative subfamilies F(ε, κ, ℵ) and G(ε, κ, ℵ) of biunivalent functions. For functions in these subfamilies, we determine the first two Maclaurin coefficient estimations |C2| and |C3|, and address the Fekete–Szeg¨o problem. Additionally, we mention some corollaries related to the main results.

     

    Keywords :

    Analytic function , Univalent and bi-univalent functions , Fekete-Szeg¨ , o problem.

    References

    [1] R. M. Ali, S. K. Lee, V. Ravichandran and S. Supramaniam, Coefficient estimates for bi-univalent Ma- Minda starlike and convex functions, Appl. Math. Lett. 25 (3) (2012), 344–351.

    [2] A. Amourah, B. A. Frasin, G. Murugusundaramoorthy, T. Al-Hawary, Bi-Bazileviˆc functions of order ϑ +iδ associated with (p; q)-Lucas polynomials. AIMS Mathematics 6.5 (2021), 4296-4305.

    [3] C. Carathe´odory, U¨ ber den Variabilita¨tsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen. Math. Ann. 1907, 64, 95–115.

    [4] H. O. Guney, G. Murugusundaramoorthy and J. Sokol, Subclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers, Acta Univ. Sapientiae, Math., 10 (2018), no. 1, 70-84.

    [5] G. Murugusundaramoorthy, Subclasses of starlike and convex functions involving Poisson distribution series, Afr. Mat., 28(2017), 1357–1366.

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

    [7] 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, no. 3-4 (2019): 495–503.

    [8] P. Zaprawa, Estimates of initial coefficients for bi-univalent functions. Abstr. Appl. Anal. 2014, 2014, 357480.

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

    [10] T. Al-Hawary, Coefficient bounds and Fekete–Szeg¨o problem for qualitative subclass of bi-univalent functions. Afrika Matematika 33 (1), 1-9.

     
    Cite This Article As :
    Al-Hawary, Tariq. , Amourah, Ala. , Salah, Jamal. , Yousef, Feras. Two Inclusive Subfamilies of bi-univalent Functions. International Journal of Neutrosophic Science, vol. , no. , 2024, pp. 315-323. DOI: https://doi.org/10.54216/IJNS.240422
    Al-Hawary, T. Amourah, A. Salah, J. Yousef, F. (2024). Two Inclusive Subfamilies of bi-univalent Functions. International Journal of Neutrosophic Science, (), 315-323. DOI: https://doi.org/10.54216/IJNS.240422
    Al-Hawary, Tariq. Amourah, Ala. Salah, Jamal. Yousef, Feras. Two Inclusive Subfamilies of bi-univalent Functions. International Journal of Neutrosophic Science , no. (2024): 315-323. DOI: https://doi.org/10.54216/IJNS.240422
    Al-Hawary, T. , Amourah, A. , Salah, J. , Yousef, F. (2024) . Two Inclusive Subfamilies of bi-univalent Functions. International Journal of Neutrosophic Science , () , 315-323 . DOI: https://doi.org/10.54216/IJNS.240422
    Al-Hawary T. , Amourah A. , Salah J. , Yousef F. [2024]. Two Inclusive Subfamilies of bi-univalent Functions. International Journal of Neutrosophic Science. (): 315-323. DOI: https://doi.org/10.54216/IJNS.240422
    Al-Hawary, T. Amourah, A. Salah, J. Yousef, F. "Two Inclusive Subfamilies of bi-univalent Functions," International Journal of Neutrosophic Science, vol. , no. , pp. 315-323, 2024. DOI: https://doi.org/10.54216/IJNS.240422

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