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

Ala Amourah (), Omar Alnajar, Maslina Darus (), Ala Shdouh and Osama Ogilat
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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

Mathematics, 2023, vol. 11, issue 8, 1-9

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.

Keywords: Gegenbauer polynomials; bell distribution; bi-univalent functions; Fekete–Szegö problem; analytic functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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