Estimates on initial coefficients of certain subclasses of bi-univalent functions associated with quasi-subordination

Patil, Amol B.; Naik, Uday

doi:10.14419/gjma.v5i1.6959

Cited by 5 publications

(13 citation statements)

References 9 publications

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“…Corollaries and ConsequencesChoosing γ = 1 and δ = 0 in Theorem 5, we get the consequences below Corollary 6 ([15]). Let the function f ∈ R q Σ (λ, φ) .…”

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confidence: 81%

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On quasi subordination for analytic and biunivalent function class

Akgul

2017

Preprint

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For two analytic functions f and F , if there exists analytic functions F and w, with |F (z)| ≤ 1, w(0) = 0 and |w(z)| < 1 such that the equality f (z) = F (z)ϕ(ω(z)) holds, then the function f is said to be quasi subordinate to ϕ, written as follows f (z) ≺q ϕ(z), z ∈ E. In this work, the subclass M q,ϕ Σ (γ, λ, δ) of the function class S of bi-univalent functions associated with the quasi-subordination is defined and studied. Also some relevant classes are recognized and connections to previus results are made.

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“…Corollaries and ConsequencesChoosing γ = 1 and δ = 0 in Theorem 5, we get the consequences below Corollary 6 ([15]). Let the function f ∈ R q Σ (λ, φ) .…”

mentioning

confidence: 81%

“…This study was firstly introduced by Patil and Naik ( [15]). The class R q Σ (λ, ϕ) containes functions f ∈ S satisfying…”

Section: Introduction and Definitionsmentioning

confidence: 99%

On quasi subordination for analytic and biunivalent function class

Akgul

2017

Preprint

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“…If a function 𝓅 ∈ 𝒫 is given by ( 4), then mates on the first two Taylor-Maclaurin coefficients were found in these subclasses (see [7][8][9][10]). Several authors introduced initial Maclaurin coefficients bounds for subclasses of bi-univalent functions (see [11,12]). Many researchers ( [11,13,14]) have studied numerous curious subclasses of the bi-univalent function class Ω and observed non-sharp bounds on the first two Taylor-Maclaurin coefficients.…”

Section: Lemma 2 ([27]mentioning

confidence: 99%

“…mates on the first two Taylor-Maclaurin coefficients were found in these subclasses (see [7][8][9][10]). Several authors introduced initial Maclaurin coefficients bounds for subclasses of bi-univalent functions (see [11,12]). Many researchers ( [11,13,14]) have studied numerous curious subclasses of the bi-univalent function class Ω and observed non-sharp bounds on the first two Taylor-Maclaurin coefficients.…”

Section: Lemma 2 ([27]mentioning

confidence: 99%

“…Noonan and Thomas [15] defined the q th Hankel determinant of f , in 1976 for n ≥ 1 and q ≥ 1 by Symmetry 2024, 16, 239 2 of 10 mates on the first two Taylor-Maclaurin coefficients were found in these subclasses (see [7][8][9][10]). Several authors introduced initial Maclaurin coefficients bounds for subclasses of bi-univalent functions (see [11,12]). Many researchers ( [11,13,14]) 2 | for the classes of bi-starlike and bi-convex ( [16][17][18][19]).…”

Section: Introductionmentioning

confidence: 99%

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On Third Hankel Determinant for Certain Subclass of Bi-Univalent Functions

Shakir,

Atshan

2024

Symmetry

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This study presents a subclass of bi-univalent functions within the open unit disk region . The objective of this class is to determine the bounds of the Hankel determinant of order 3, (). In this study, new constraints for the estimates of the third Hankel determinant for the class are presented, which are of considerable interest in various fields of mathematics, including complex analysis and geometric function theory. Here, we define these bi-univalent functions as and impose constraints on the coefficients . Our investigation provides the upper bounds for the bi-univalent functions in this newly developed subclass, specifically for n = 2, 3, 4, and 5. We then derive the third Hankel determinant for this particular class, which reveals several intriguing scenarios. These findings contribute to the broader understanding of bi-univalent functions and their potential applications in diverse mathematical contexts. Notably, the results obtained may serve as a foundation for future investigations into the properties and applications of bi-univalent functions and their subclasses.

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On sharp bounds of Fekete-Szegő functional for a certain bi-univalent function class associated with quasi-subordination

Patil¹

2022

Afr. Mat.

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Estimates on initial coefficients of certain subclasses of bi-univalent functions associated with quasi-subordination

Cited by 5 publications

References 9 publications

On quasi subordination for analytic and biunivalent function class

On quasi subordination for analytic and biunivalent function class

On Third Hankel Determinant for Certain Subclass of Bi-Univalent Functions

On sharp bounds of Fekete-Szegő functional for a certain bi-univalent function class associated with quasi-subordination

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