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Estimates for the Coefficients of Subclasses Defined by the Bell Distribution of Bi-Univalent Functions Subordinate to Gegenbauer Polynomials

Author

Listed:
  • Ala Amourah

    (Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 21110, Jordan)

  • Omar Alnajar

    (Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia)

  • Maslina Darus

    (Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia)

  • Ala Shdouh

    (Faculty General Education and Foundation Program, Rabdan Academy, Abu Dhabi 00971, United Arab Emirates)

  • Osama Ogilat

    (Department of Basic Sciences, Faculty of Arts and Science, Al-Ahliyya Amman University, Amman 19328, Jordan)

Abstract

In the real world there are many applications that find the Bell distribution to be a useful and relevant model. One of these is the normal distribution. In this paper, we develop a new subclass of analytic bi-univalent functions by making use of the Bell distribution as a building block. These functions involve the Gegenbauer polynomials, and we use them to establish our new subclass. In this study, we solve the Fekete–Szegö functional problem and analyse various different estimates of the Maclaurin coefficients D 2 and D 3 for functions that belong to the built class.

Suggested Citation

  • Ala Amourah & Omar Alnajar & Maslina Darus & Ala Shdouh & Osama Ogilat, 2023. "Estimates for the Coefficients of Subclasses Defined by the Bell Distribution of Bi-Univalent Functions Subordinate to Gegenbauer Polynomials," Mathematics, MDPI, vol. 11(8), pages 1-9, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1799-:d:1120132
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    References listed on IDEAS

    as
    1. Ala Amourah & Mohammad Alomari & Feras Yousef & Abdullah Alsoboh & Ismail Shah, 2022. "Consolidation of a Certain Discrete Probability Distribution with a Subclass of Bi-Univalent Functions Involving Gegenbauer Polynomials," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-6, May.
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