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Research Article | Open Access

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

Abeer O. Badghaish1, Abdel Moneim Y. Lashin1,2( ), Amani Z. Bajamal1, Fayzah A. Alshehri1
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Department of Mathematics Faculty of Science, Mansoura University, Mansoura, 35516, Egypt
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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 | A 2 | and | A 3 | 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.

Keywords

bi-univalent functionsanalytic functionsstarlike and convex functionsLegendre polynomials
CLC number: 30C45, 30C50, 30C55

References

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AIMS Mathematics
Volume 8 Issue 10,
October 2023
Pages 23534-23547
DOI: 10.3934/math.20231196

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Cite this article:
Badghaish AO, Lashin AMY, Bajamal AZ, et al. A new subclass of analytic and bi-univalent functions associated with Legendre polynomials. AIMS Mathematics, 2023, 8(10): 23534-23547. https://doi.org/10.3934/math.20231196

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Received: 08 May 2023
Revised: 18 July 2023
Accepted: 24 July 2023
Published: 15 October 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)