A new subclass of analytic and bi-univalent functions associated with Legendre polynomials

Abeer O. Badghaish; Abdel Moneim Y. Lashin; Amani Z. Bajamal; Fayzah A. Alshehri; Abeer O. Badghaish; Abdel Moneim Y. Lashin; Amani Z. Bajamal; Fayzah A. Alshehri

doi:10.3934/math.20231196

AIMS Mathematics

2023, Volume 8, Issue 10: 23534-23547. doi: 10.3934/math.20231196

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A new subclass of analytic and bi-univalent functions associated with Legendre polynomials

1.
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2.
Department of Mathematics Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

Received: 08 May 2023 Revised: 18 July 2023 Accepted: 24 July 2023 Published: 28 July 2023
MSC : 30C45, 30C50, 30C55

In this paper, we introduce a new subclass of analytic and bi-univalent functions in the open unit disc $ U. $ For this subclass of functions, estimates of the initial coefficients $ \left\vert A_{2}\right\vert $ and $ \left\vert A_{3}\right\vert $ of the Taylor-Maclaurin series are given. An application of Legendre polynomials to this subclass of functions is presented. Furthermore, our study discusses several special cases.
- bi-univalent functions,
- analytic functions,
- starlike and convex functions,
- Legendre polynomials
Citation: Abeer O. Badghaish, Abdel Moneim Y. Lashin, Amani Z. Bajamal, Fayzah A. Alshehri. A new subclass of analytic and bi-univalent functions associated with Legendre polynomials[J]. AIMS Mathematics, 2023, 8(10): 23534-23547. doi: 10.3934/math.20231196

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Abstract

In this paper, we introduce a new subclass of analytic and bi-univalent functions in the open unit disc $ U. $ For this subclass of functions, estimates of the initial coefficients $ \left\vert A_{2}\right\vert $ and $ \left\vert A_{3}\right\vert $ of the Taylor-Maclaurin series are given. An application of Legendre polynomials to this subclass of functions is presented. Furthermore, our study discusses several special cases.

References

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