• Title, Summary, Keyword: univalent functions

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ON UNIVALENT SUBORDINATE FUNCTIONS

  • Park, Suk-Joo
    • The Pure and Applied Mathematics
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    • v.3 no.2
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    • pp.103-111
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    • 1996
  • Let $f(z)=z+\alpha_2 z^2$+…+ \alpha_{n}z^n$+… be regular and univalent in $\Delta$ = {z : │z│<1}. In this paper, using the proper subordinate functions, we investigate the some relations between subordinations and conditions of functions belonging to subclasses of univalent functions.

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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.

UNIVALENT FUNCTIONS WITH POSITIVE COEFFICIENTS INVOLVING POISSON DISTRIBUTION SERIES

  • Murugusundaramoorthy, Gangadharan
    • Honam Mathematical Journal
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    • v.40 no.3
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    • pp.529-538
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    • 2018
  • The purpose of the present paper is to establish connections between various subclasses of analytic univalent functions by applying certain convolution operator involving Poisson distribution series. To be more precise,we investigate such connections with the classes of analytic univalent functions with positive coefficients in the open unit disk.

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.

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.

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.

Partial Sums of Starlike Harmonic Univalent Functions

  • Porwal, Saurabh;Dixit, Kaushal Kishore
    • Kyungpook Mathematical Journal
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    • v.50 no.3
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    • pp.433-445
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    • 2010
  • Although, interesting properties on the partial sums of analytic univalent functions have been investigated extensively by several researchers, yet analogous results on partial sums of harmonic univalent functions have not been so far explored. The main purpose of the present paper is to establish some new and interesting results on the ratio of starlike harmonic univalent function to its sequences of partial sums.

UNIFORMLY LOCALLY UNIVALENT FUNCTIONS

  • Song, Tai-Sung
    • 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.

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