Bounds for Two New Subclasses of Bi-Univalent Functions Associated with Legendre Polynomials

Lashin, A. Y.; Badghaish, Abeer O.; Bajamal, Amani Z.

doi:10.3390/math9243188

Cited by 2 publications

(1 citation statement)

References 22 publications

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“…All studies aim to determine more accurate estimations on the coefficients of these functions. Certain subclasses of the bi-univalent functions were identified based on specific properties and or conditions that enable more precise evaluations of their coefficients (see [26][27][28][29][30][31][32][33]). In this article, we consider a particular subclass of the bi-univalent functions subordinate to GPs to derive upper bounds for the Taylor-Maclaurin coefficients, | a 2 | and | a 3 |, and determine the greatest value of the Fekete-Szegö functional F η ( f ).…”

Section: Introductionmentioning

confidence: 99%

Coefficients and Fekete–Szegö Functional Estimations of Bi-Univalent Subclasses Based on Gegenbauer Polynomials

Hussen

Zeyani

2023

Mathematics

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Subclasses of analytic and bi-univalent functions have been extensively improved and utilized for estimating the Taylor–Maclaurin coefficients and the Fekete–Szegö functional. In this paper, we consider a certain subclass of normalized analytic and bi-univalent functions. These functions have inverses that possess a bi-univalent analytic continuation to an open unit disk and are associated with orthogonal polynomials; namely, Gegenbauer polynomials that satisfy subordination conditions on the open unit disk. We use this subclass to derive new approximations for the second and third Taylor–Maclaurin coefficients and the Fekete–Szegö functional. Furthermore, we discuss several new results that arise when we specialize the parameters used in our fundamental findings.

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Section: Introductionmentioning

confidence: 99%

Coefficients and Fekete–Szegö Functional Estimations of Bi-Univalent Subclasses Based on Gegenbauer Polynomials

Hussen

Zeyani

2023

Mathematics

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

Badghaish,

Lashin,

Bajamal

et al. 2023

MATH

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<abstract><p>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.</p></abstract>

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Bounds for Two New Subclasses of Bi-Univalent Functions Associated with Legendre Polynomials

Abstract: In this article, two new subclasses of the bi-univalent function class σ related with Legendre polynomials are presented. Additionally, the first two Taylor–Maclaurin coefficients a2 and a3 for the functions belonging to these new subclasses are estimated.

Cited by 2 publications

References 22 publications

Coefficients and Fekete–Szegö Functional Estimations of Bi-Univalent Subclasses Based on Gegenbauer Polynomials

Coefficients and Fekete–Szegö Functional Estimations of Bi-Univalent Subclasses Based on Gegenbauer Polynomials

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

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