• Title/Summary/Keyword: differential subordination

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Integral operators that preserve the subordination

  • Bulboaca, Teodor
    • Bulletin of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.627-636
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    • 1997
  • Let $H(U)$ be the space of all analytic functions in the unit disk $U$ and let $K \subset H(U)$. For the operator $A_{\beta,\gamma} : K \longrightarrow H(U)$ defined by $$ A_{\beta,\gamma}(f)(z) = [\frac{z^\gamma}{\beta + \gamma} \int_{0}^{z} f^\beta (t)t^{\gamma-1} dt]^{1/\beta} $$ and $\beta,\gamma \in C$, we determined conditions on g(z), $\beta and \gamma$ such that $$ z[\frac{z}{f(z)]^\beta \prec z[\frac{z}{g(z)]^\beta implies z[\frac{z}{A_{\beta,\gamma}(f)(z)]^\beta \prec z[\frac{z}{A_{\beta,\gamma}(g)(z)]^\beta $$ and we presented some particular cases of our main result.

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Classes of Multivalent Functions Defined by Dziok-Srivastava Linear Operator and Multiplier Transformation

  • Kumar, S. Sivaprasad;Taneja, H.C.;Ravichandran, V.
    • Kyungpook Mathematical Journal
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    • v.46 no.1
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    • pp.97-109
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    • 2006
  • In this paper, the authors introduce new classes of p-valent functions defined by Dziok-Srivastava linear operator and the multiplier transformation and study their properties by using certain first order differential subordination and superordination. Also certain inclusion relations are established and an integral transform is discussed.

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COEFFICIENT BOUNDS FOR CLOSE-TO-CONVEX FUNCTIONS ASSOCIATED WITH VERTICAL STRIP DOMAIN

  • Bulut, Serap
    • Communications of the Korean Mathematical Society
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    • v.35 no.3
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    • pp.789-797
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    • 2020
  • By considering a certain univalent function in the open unit disk 𝕌, that maps 𝕌 onto a strip domain, we introduce a new class of analytic and close-to-convex functions by means of a certain non-homogeneous Cauchy-Euler-type differential equation. We determine the coefficient bounds for functions in this new class. Relevant connections of some of the results obtained with those in earlier works are also provided.

ON CERTAIN CLASSES OF MULTIVALENT FUNCTIONS INVOLVING A GENERALIZED DIFFERENTIAL OPERATOR

  • Selvaraj, Chellian;Selvakumaran, Kuppathai A.
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.5
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    • pp.905-915
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    • 2009
  • Making use of a generalized differential operator we introduce some new subclasses of multivalent analytic functions in the open unit disk and investigate their inclusion relationships. Some integral preserving properties of these subclasses are also discussed.

ON SANDWICH THEOREMS FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING CARLSON-SHAFFER OPERATOR

  • Shanmugam, Tirunelveli Nellaiappan;Srikandan, Sivasubramanian;Frasin, Basem Aref;Kavitha, Seetharaman
    • Journal of the Korean Mathematical Society
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    • v.45 no.3
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    • pp.611-620
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    • 2008
  • The purpose of this present paper is to derive some subordination and superordination results involving Carlson-Shaffer operator for certain normalized analytic functions in the open unit disk. Relevant connections of the results, which are presented in the paper, with various known results are also considered.

Differential Subordinations and Superordinations of Certain Meromorphic Functions associated with an Integral Operator

  • DARWISH, HANAN ELSAYED;LASHIN, ABD AL-MONEM YOUSOF;SOILEH, SOLIMAN MOHAMMED
    • Kyungpook Mathematical Journal
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    • v.55 no.3
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    • pp.625-639
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    • 2015
  • Differential subordinations and superordinations results are obtained for certain meromorphic functions in the punctured unit disk which are associated with an integral operator. These results are obtained by investigating appropriate classes of a dmissible functions. Sandwich-type results are also obtained.

Some properties of a Certain family of Meromorphically Univalent Functions defined by an Integral Operator

  • Aghalary, Rasoul
    • Kyungpook Mathematical Journal
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    • v.48 no.3
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    • pp.379-385
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    • 2008
  • Making use of a linear operator, we introduce certain subclass of meromorphically univalent functions in the punctured unit disk and study its properties including some inclusion results, coefficient and distortion problems. Our result generalize many results known in the literature.

On Subclasses of P-Valent Analytic Functions Defined by Integral Operators

  • Aghalary, Rasoul
    • Kyungpook Mathematical Journal
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    • v.47 no.3
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    • pp.393-401
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    • 2007
  • In the present paper we introduce the subclass $S^{\lambda}_{a,c}(p,A,B)$ of analytic functions and then we investigate some interesting properties of functions belonging to this subclass. Our results generalize many results known in the literature and especially generalize some of the results obtained by Ling and Liu [5].

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THE BRIOT-BOUQUET DIFFERENTIAL SUBORDINATION ASSOCIATED WITH VERTICAL STRIP DOMAINS

  • Sim, Young Jae;Kwon, Oh Sang
    • Honam Mathematical Journal
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    • v.39 no.4
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    • pp.503-514
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    • 2017
  • For real parameters ${\alpha}$ and ${\beta}$ such that ${\alpha}$ < 1 < ${\beta}$, we denote by $\mathcal{P}({\alpha},{\beta})$ the class of analytic functions p, which satisfy p(0) = 1 and ${\alpha}$ < ${\Re}\{p(z)\}$ < ${\beta}$ in ${\mathbb{D}}$, where ${\mathbb{D}}$ denotes the open unit disk. Let ${\mathcal{A}}$ be the class of analytic functions in ${\mathbb{D}}$ such that f(0) = 0 = f'(0) - 1. For $f{\in}{\mathcal{A}}$, ${\mu}{\in}{\mathbb{C}}{\backslash}\{0\}$ and ${\nu}{\in}{\mathbb{C}}$, let $I_{{\mu},{\nu}:{\mathcal{A}}{\rightarrow}{\mathcal{A}}$ be an integral operator defined by $$I_{{\mu},{\nu}[f](z)}=\({\frac{{\mu}+{\nu}}{z^{\nu}}}{\int}^z_0f^{\mu}(t)t^{{\nu}-1}dt\)^{1/{\mu}}$$. In this paper, we find some sufficient conditions on functions to be in the class $\mathcal{P}({\alpha},{\beta})$. One of these results is applied to the integral operator $I_{{\mu},{\nu}}$ of two classes of starlike functions which are related to the class $\mathcal{P}({\alpha},{\beta})$.