• Korean Journal of Mathematics
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• 제32권1호
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• pp.183-193
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• 2024

In this paper, a new class of bi-univalent functions that are described by Gegenbauer polynomials is presented. We obtain the estimates of the Taylor-Maclaurin coefficients |m₂| and |m₃| for each function in this class of bi-univalent functions. In addition, the Fekete-Szegö problems function new are also studied.

• 호남수학학술지
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• 제39권4호
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• pp.591-601
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• 2017

In this paper, by means of the $S{\breve{a}}l{\breve{a}}gean$ operator, we introduce a new subclass $\mathcal{B}^{m,n}_{\Sigma}({\gamma};{\varphi})$ of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$. For functions belonging to this class, we consider Fekete-$Szeg{\ddot{o}}$ inequalities.

• 대한수학회논문집
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• 제34권3호
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• pp.783-797
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• 2019

In this paper, we introduce and investigate a subclass ${\Im}_{\Sigma}({\alpha},{\beta},{\gamma})$ of analytic and bi-univalent functions of complex order in the open unit disk U in complex plane. Here, we obtain an upper bound for the second Hankel determinant of the functions belonging to this class. Moreover, several interesting conclusions of the results obtained here are also discussed.

• 대한수학회보
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• 제55권2호
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• pp.405-413
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• 2018

In this work, we use the Faber polynomial expansions to find upper bounds for the coefficients of analytic bi-univalent functions in subclass $\Sigma({\tau},{\gamma},{\varphi})$ which is defined by subordination conditions in the open unit disk ${\mathbb{U}}$. In certain cases, our estimates improve some of those existing coefficient bounds.

• 대한수학회보
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• 제50권5호
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• pp.1531-1538
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• 2013

In the present investigation, the author introduces two interesting subclasses of normalized meromorphic univalent functions $w=f(z)$ defined on $\tilde{\Delta}:=\{z{\in}\mathbb{C}:1<{\mid}z{\mid}<{\infty}\}$ whose inverse $f^{-1}(w)$ is also univalent meromorphic in $\tilde{\Delta}$. Estimates for the initial coefficients are obtained for the functions in these new subclasses.

• 대한수학회논문집
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• 제33권4호
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• pp.1229-1237
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• 2018

In this paper, we obtain the coefficient bounds for subclass of meromorphic bi-univalent functions by using the Faber polynomial expansions. The results presented in this paper would generalize and improve some recent works.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.1035-1041
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• 2022

Herein, we construct a qualitative subclass B^γ(κ, µ, σ) of the class of analytic bi-univalent functions. Next, we explore estimates of the coefficients |a_j| (j = 1, 2) and the Fekete-Szegö functional |a₃ - ςa²₂| for functions in this subclass.

• East Asian mathematical journal
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• 제32권1호
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• pp.47-59
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• 2016

The purpose of the present paper is to introduce and investigate two new subclasses of bi-univalent functions of complex order defined in the open unit disk, which are associated with Hurwitz-Lerch zeta function and satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients ${\mid}a_2{\mid}$ and ${\mid}a_3{\mid}$ for functions in the new subclasses. Several (known or new) consequences of the results are also pointed out.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.519-526
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• 2021

In a very recent paper, Yousef et al. [Anal. Math. Phys. 11: 58 (2021)] introduced two new subclasses of analytic and bi-univalent functions and obtained the estimates on the first two Taylor-Maclaurin coefficients |a₂| and |a₃| for functions belonging to these classes. In this study, we introduce a general subclass 𝔅^h,p_Σ(λ, μ, 𝛿) of analytic and bi-univalent functions in the unit disk 𝕌, and investigate the coefficient bounds for functions belonging to this general function class. Our results improve the results of the above mentioned paper of Yousef et al.

• 대한수학회논문집
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• 제37권1호
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• pp.113-123
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• 2022

In the present paper, we introduce the subclasses 𝔅_1Σ(𝜇), B_1Σ(𝜇, 𝛾) and U_Σ(𝜇, 𝛾) of bi-univalent Bazilevič functions which are defined in the open unit disk 𝔻. Further, we obtain sharp estimates on initial coefficients a₂, a₃, a₄ and also sharp estimate on the Fekete-Szegö functional a₃ - ka²₂ for the functions belong to these subclasses.