Second Hankel Determinant for a Certain Subclass of Bi-Close to Convex Functions Defined by Kaplan

Kanas, S.; Sivasankari, Pesse V.; Karthiyayini, Roy; Sivasubramanian, S.

doi:10.3390/sym13040567

Cited by 4 publications

(3 citation statements)

References 22 publications

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“…Proof. Let g, ψ and φ be given in the form (20), ( 21) and (22). Since h ∈ K Σ (k, γ), there exists analytic functions p, q with…”

Section: Coefficient Bounds For Kmentioning

confidence: 99%

“…The bounds on |a n |(n = 2, 3) for the class S * Σ (γ) and C Σ (γ) (for details, see [10]) were established and non-sharp. Subsequent to Brannan and Taha [10], lots of researchers (see [13][14][15][16][17][18][19][20][21][22]) in recent times have introduced and investigated several interesting subclasses of the class Σ. They have obtained bounds on the initial two Taylor-Maclaurin coefficients for the new bi-univalent classes they introduced and were identified as non-sharp.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On a New Class of Bi-Close-to-Convex Functions with Bounded Boundary Rotation

Breaz,

Sharma,

Sivasubramanian

et al. 2023

Mathematics

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In the current article, we introduce a new class of bi-close-to-convex functions with bounded boundary rotation. For this new class, the authors obtain the first three initial coefficient bounds of the newly defined bi-close-to-convex functions with bounded boundary rotation. By choosing special bi-convex functions, the authors obtain the first three initial coefficient bounds in the last section. The authors also verify the special cases where the familiar Brannan and Clunie’s conjecture is satisfied. Furthermore, the famous Fekete–Szegö inequality is also obtained for this new class of functions. Apart from the new interesting results, some of the results presented here improves the earlier results existing in the literature.

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“…Proof. Let g, ψ and φ be given in the form (20), ( 21) and (22). Since h ∈ K Σ (k, γ), there exists analytic functions p, q with…”

Section: Coefficient Bounds For Kmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On a New Class of Bi-Close-to-Convex Functions with Bounded Boundary Rotation

Breaz,

Sharma,

Sivasubramanian

et al. 2023

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Let Σ denote the class of all functions f ∈ A that are bi-univalent in U given by (7). For interesting subclasses of functions in the class Σ, see [14][15][16][17][18][19]. Now, let us define the linear operator…”

Section: Definitionmentioning

confidence: 99%

Exploiting the Pascal Distribution Series and Gegenbauer Polynomials to Construct and Study a New Subclass of Analytic Bi-Univalent Functions

et al. 2022

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In the present analysis, we aim to construct a new subclass of analytic bi-univalent functions defined on symmetric domain by means of the Pascal distribution series and Gegenbauer polynomials. Thereafter, we provide estimates of Taylor–Maclaurin coefficients a2 and a3 for functions in the aforementioned class, and next, we solve the Fekete–Szegö functional problem. Moreover, some interesting findings for new subclasses of analytic bi-univalent functions will emerge by reducing the parameters in our main results.

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An Avant-Garde Construction for Subclasses of Analytic Bi-Univalent Functions

Yousef

Amourah

Frasin

et al. 2022

Axioms

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The zero-truncated Poisson distribution is an important and appropriate model for many real-world applications. Here, we exploit the zero-truncated Poisson distribution probabilities to construct a new subclass of analytic bi-univalent functions involving Gegenbauer polynomials. For functions in the constructed class, we explore estimates of Taylor–Maclaurin coefficients a2 and a3, and next, we solve the Fekete–Szegő functional problem. A number of new interesting results are presented to follow upon specializing the parameters involved in our main results.

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Second Hankel Determinant for a Certain Subclass of Bi-Close to Convex Functions Defined by Kaplan

Cited by 4 publications

References 22 publications

On a New Class of Bi-Close-to-Convex Functions with Bounded Boundary Rotation

On a New Class of Bi-Close-to-Convex Functions with Bounded Boundary Rotation

Exploiting the Pascal Distribution Series and Gegenbauer Polynomials to Construct and Study a New Subclass of Analytic Bi-Univalent Functions

An Avant-Garde Construction for Subclasses of Analytic Bi-Univalent Functions

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