Fekete‐Szegö Functional for Bi‐univalent Functions Related with Gegenbauer Polynomials

Ahmad, Ibrar; Shah, Syed Ghoos Ali; Hussain, Saqib; Darus, Maslina; Ahmad, Babar

doi:10.1155/2022/2705203

Cited by 8 publications

(4 citation statements)

References 18 publications

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“…A new family of holomorphic and bi-univalent functions is introduced using a new operator joining Poisson distribution with a Ruscheweyh derivative operator and upper bounds for the second and third coefficients are discussed in [17]. Other similar very recent studies can be seen in [18][19][20].…”

Section: Introduction and Definitionsmentioning

confidence: 86%

New Applications of Faber Polynomial Expansion for Analytical Bi-Close-to-Convex Functions Defined by Using q-Calculus

et al. 2023

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In this investigation, the q-difference operator and the Sălăgean q-differential operator are utilized to establish novel subclasses of analytical bi-close-to-convex functions. We determine the general Taylor–Maclaurin coefficient of the functions in this class using the Faber polynomial method. We demonstrate the unpredictable behaviour of initial coefficients a2, a3 and investigate the Fekete–Szegő problem a3−a22 for the subclasses of bi-close-to-convex functions. To highlight the connections between existing knowledge and new research, certain known and unknown corollaries are also highlighted.

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Section: Introduction and Definitionsmentioning

confidence: 86%

New Applications of Faber Polynomial Expansion for Analytical Bi-Close-to-Convex Functions Defined by Using q-Calculus

et al. 2023

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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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“…For various subclasses of bi-univalent functions, see, for example, [14][15][16][17][18][19][20][21][22][23][24][25][26]. Definition 4.…”

Section: Introductionmentioning

confidence: 99%

Coefficient Estimates for Certain Families of Analytic Functions Associated with Faber Polynomial

Attiya

Albalahi

Hassan

2023

Journal of Function Spaces

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In this paper, we use the Faber polynomial expansion to obtain bounds for the general coefficients a n of bi-univalent functions in the family of analytic functions in the open unit disk. Estimation of the bound value for the initial coefficients of the functions in these classes is also established.

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Fekete‐Szegö Functional for Bi‐univalent Functions Related with Gegenbauer Polynomials

Cited by 8 publications

References 18 publications

New Applications of Faber Polynomial Expansion for Analytical Bi-Close-to-Convex Functions Defined by Using q-Calculus

New Applications of Faber Polynomial Expansion for Analytical Bi-Close-to-Convex Functions Defined by Using q-Calculus

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

Coefficient Estimates for Certain Families of Analytic Functions Associated with Faber Polynomial

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