Estimates for the Coefficients of Subclasses Defined by the Bell Distribution of Bi-Univalent Functions Subordinate to Gegenbauer Polynomials-Reference-Cited by-同舟云学术

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

Published:2023-04-10 Issue:8 Volume:11 Page:1799
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Amourah Ala¹^ORCID,Alnajar Omar²^ORCID,Darus Maslina²^ORCID,Shdouh Ala³,Ogilat Osama⁴^ORCID

Affiliation:

1. Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 21110, Jordan

2. Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia

3. Faculty General Education and Foundation Program, Rabdan Academy, Abu Dhabi 00971, United Arab Emirates

4. 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 D2 and D3 for functions that belong to the built class.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/8/1799/pdf

Reference33 articles.

1. Legendre, A. (1785). Recherches sur Laattraction des Sphéroides Homogénes, Académie des Sciences de laInstitut de France.

2. Bateman, H. (1953). Higher Transcendental Functions, McGraw-Hill.

3. Eine Bemerkung Ãber ungerade schlichte Funktionen;Fekete;J. Lond. Math. Soc.,1933

4. On a Coefficient problem for bi-univalent functions;Lewin;Proc. Amer. Math. Soc. USA,1967

5. Illafe, M., Yousef, F., Haji Mohd, M., and Supramaniam, S. (2023). Initial Coefficients Estimates and Fekete–Szego Inequality Problem for a General Subclass of Bi-Univalent Functions Defined by Subordination. Axioms, 12.

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The Miller-Ross Poisson distribution and its applications to certain classes of bi-univalent functions related to Horadam polynomials;Heliyon;2024-04

2. APPLICATION OF GEGENBAUER POLYNOMIALS TO CERTAIN CLASSES OF BI-UNIVALENT FUNCTIONS OF ORDER ν;KOREAN J MATH;2024

3. Coefficient estimates for subclasses of bi-univalent functions related to Gegenbauer polynomials and an application of bell distribution;AIP Conference Proceedings;2024

4. Coefficients and Fekete–Szegö Functional Estimations of Bi-Univalent Subclasses Based on Gegenbauer Polynomials;Mathematics;2023-06-25

5. Certain Subclasses of Analytic and Bi-Univalent Functions Governed by the Gegenbauer Polynomials Linked with q-Derivative;Symmetry;2023-06-02