• Journal of applied mathematics & informatics
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• v.40 no.5_6
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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.

• The Pure and Applied Mathematics
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• v.6 no.2
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• pp.87-93
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• 1999

A holomorphic function f on D = {z : │z│ ＜ 1} is called uniformly locally univalent if there exists a positive constant $\rho$ such that f is univalent in every hyperbolic disk of hyperbolic radius $\rho$. We establish a characterization of uniformly locally univalent functions and investigate uniform local univalence of holomorphic universal covering projections.

• Kyungpook Mathematical Journal
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• v.18 no.1
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• pp.53-59
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• 1978

The coefficient problems of univalent functions was given by Bieberbach. As is well-known, Koebe distortion theorem has close connection with the coefficient problems of univalent functions. It is purpose of this paper to give the distortion theorems for fractional integral and derivative of univalent functions.

• 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 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.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.543-552
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• 2006

The purpose of the present paper is to introduce two novel subclasses $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$ and $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions with negative coefficients, involving Ruscheweyh derivative operator. The various results investigated in this paper include coefficient estimates, distortion inequalities, radii of close-to-convexity, starlikenes, and convexity for the functions belonging to the class $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$. These results are then appropriately applied to derive similar geometrical properties for the other class $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions. Relevant connections of these results with those in several earlier investigations are briefly indicated.

• 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_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.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.495-505
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• 2018

The purpose of the present paper is to investigate Confluent hypergeometric distribution. We obtain some basic properties of this distribution. It is worthy to note that the Poisson distribution is a particular case of this distribution. Finally, we give a nice application of this distribution on certain classes of univalent functions of the conic regions.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.493-503
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• 2019

In the present investigation, we define two new subclasses of analytic and m-fold symmetric bi-univalent functions defined by a linear combination in the open unit disk U. Furthermore, for functions in each of the subclasses introduced here, we establish upper bounds for the initial coefficients ${\mid}a_{m+1}{\mid}$ and ${\mid}a_{2m+1}{\mid}$. Also, we indicate certain special cases for our results.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.567-592
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• 2014

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notions of harmonic Alexander operator and harmonic Libera operator are introduced and their properties are investigated.

• 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.