Necessary and Sufficient Conditions for Normalized Wright Functions to Be in Certain Classes of Analytic Functions

Al-Hawary, Tariq; Aldawish, Ibtisam; Frasin, B. A.; Alkam, Osama; Yousef, Feras

doi:10.3390/math10244693

Cited by 4 publications

(2 citation statements)

References 25 publications

(26 reference statements)

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“…The set of Gegenbauer polynomials is a general subclass of Jacobi polynomials. For fundamental definitions and some important properties, the readers are referred to [16][17][18][19], and for neoteric investigations that connect geometric function theory with the classical orthogonal polynomials, see [20][21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Initial Coefficients Estimates and Fekete–Szegö Inequality Problem for a General Subclass of Bi-Univalent Functions Defined by Subordination

Illafe

Yousef

Mohd

et al. 2023

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In the present work, we aim to introduce and investigate a novel comprehensive subclass of normalized analytic bi-univalent functions involving Gegenbauer polynomials and the zero-truncated Poisson distribution. For functions in the aforementioned class, we find upper estimates of the second and third Taylor–Maclaurin coefficients, and then we solve the Fekete–Szegö functional problem. Moreover, by setting the values of the parameters included in our main results, we obtain several links to some of the earlier known findings.

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Section: Introductionmentioning

confidence: 99%

Initial Coefficients Estimates and Fekete–Szegö Inequality Problem for a General Subclass of Bi-Univalent Functions Defined by Subordination

Illafe

Yousef

Mohd

et al. 2023

Axioms

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“…Recently, a multitude of authors have made significant strides in establishing tight coefficient bounds for diverse subclasses of bi-univalent functions, often intertwined with specific polynomial families, (see [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]).…”

Section: Introductionmentioning

confidence: 99%

Coefficient Bounds for a Certain Subclass of Bi-Univalent Functions Associated with Lucas-Balancing Polynomials

Hussen,

Illafe

2023

Mathematics

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In this paper, we introduce a new subclass of bi-univalent functions defined using Lucas-Balancing polynomials. For functions in each of these bi-univalent function subclasses, we derive estimates for the Taylor–Maclaurin coefficients a2 and a3 and address the Fekete–Szegö functional problems for functions belonging to this new subclass. We demonstrate that several new results can be derived by specializing the parameters in our main findings. The results obtained from this study will enrich the theoretical foundation of this field and open new avenues for mathematical inquiry and application.

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Coefficient Estimation Utilizing the Faber Polynomial for a Subfamily of Bi-Univalent Functions

Alsoboh

Amourah

Sakar

et al. 2023

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The paper introduces a new family of analytic bi-univalent functions that are injective and possess analytic inverses, by employing a q-analogue of the derivative operator. Moreover, the article establishes the upper bounds of the Taylor–Maclaurin coefficients of these functions, which can aid in approximating the accuracy of approximations using a finite number of terms. The upper bounds are obtained by approximating analytic functions using Faber polynomial expansions. These bounds apply to both the initial few coefficients and all coefficients in the series, making them general and early, respectively.

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Necessary and Sufficient Conditions for Normalized Wright Functions to Be in Certain Classes of Analytic Functions

Cited by 4 publications

References 25 publications

Initial Coefficients Estimates and Fekete–Szegö Inequality Problem for a General Subclass of Bi-Univalent Functions Defined by Subordination

Initial Coefficients Estimates and Fekete–Szegö Inequality Problem for a General Subclass of Bi-Univalent Functions Defined by Subordination

Coefficient Bounds for a Certain Subclass of Bi-Univalent Functions Associated with Lucas-Balancing Polynomials

Coefficient Estimation Utilizing the Faber Polynomial for a Subfamily of Bi-Univalent Functions

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