• Title/Summary/Keyword: Bi-univalent functions

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FEKETE-SZEGÖ INEQUALITIES FOR A SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS DEFINED BY SĂLĂGEAN OPERATOR

  • BULUT, Serap
    • Honam Mathematical Journal
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    • v.39 no.4
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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.

UPPER BOUND OF SECOND HANKEL DETERMINANT FOR A SUBCLASS OF BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER

  • Mustafa, Nizami
    • Communications of the Korean Mathematical Society
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    • v.34 no.3
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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.

COEFFICIENT BOUNDS FOR CERTAIN SUBCLASSES OF MEROMORPHIC AND BI-UNIVALENT FUNCTIONS

  • Panigrahi, Trailokya
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.5
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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.

COEFFICIENT ESTIMATES FOR A SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS

  • Adegani, Ebrahim Analouei;Bulut, Serap;Zireh, Ahmad
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.2
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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.

BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER BASED ON SUBORDINATE CONDITIONS INVOLVING HURWITZ-LERCH ZETA FUNCTION

  • Murugusundaramoorthy, G.;Janani, T.;Cho, Nak Eun
    • East Asian mathematical journal
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    • v.32 no.1
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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.

COEFFICIENT ESTIMATES FOR A NEW GENERAL SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS

  • Bulut, Serap
    • Korean Journal of Mathematics
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    • v.29 no.3
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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 𝔅h,pΣ(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.

SHARP COEFFICIENT INEQUALITIES FOR CERTAIN SUBCLASSES OF BI-UNIVALENT BAZILEVIČ FUNCTIONS

  • Patil, Amol Bhausaheb
    • Communications of the Korean Mathematical Society
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    • v.37 no.1
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    • pp.113-123
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    • 2022
  • In the present paper, we introduce the subclasses 𝔅(𝜇), B(𝜇, 𝛾) and UΣ(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.

COEFFICIENT ESTIMATES FOR CERTAIN SUBCLASS OF MEROMORPHIC AND BI-UNIVALENT FUNCTIONS

  • Salehian, Safa;Zireh, Ahmad
    • Communications of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.389-397
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    • 2017
  • In this paper, we introduce and investigate an interesting subclass of meromorphic bi-univalent functions defined on ${\Delta}=\{z{\in}{\mathbb{C}}$ : 1 < |z| < ${\infty}\}$. For functions belonging to this class, estimates on the initial coefficients are obtained. The results presented in this paper would generalize and improve some recent works of several earlier authors.