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Multiplier transformations and strongly close-to-convex functions
조낙은,김태화 대한수학회 2003 대한수학회보 Vol.40 No.3
The purpose of the present paper is to introduce somenew subclasses of strongly close-to-convex functions in the openunit disk defined by multiplier transformations and study theirproperties. Our results include several previous known results asspecial cases.
조낙은,권오상 영남수학회 2011 East Asian mathematical journal Vol.27 No.3
The purpose of the present paper is to obtain some subordination and superordination preserving properties involving a certain family of multiplier transformations for meromorphic functions in the open unit disk. The sandwich-type theorems for these linear operators are also considered.
SUBORDINATION PROPERTIES FOR MULTIVALENT FUNCTIONS DEFINED BY A LINEAR OPERATOR
조낙은 장전수학회 2013 Proceedings of the Jangjeon mathematical society Vol.16 No.2
The purpose of the present paper is to investigate subordinationand superordination properties for multivalent functions in theopen unit disk associated with a linear operator with the sandwich-typetheorems. Moreover, we give an application of the main results to theGauss hypergeometric function.
조낙은 장전수학회 2013 Proceedings of the Jangjeon mathematical society Vol.16 No.3
The purpose of the present paper is to investigate somesubordination- and superordination- preserving properties for multivalentfunctions in the open unit disk associated with a family of multipliertransformations. The sandwich-type theorems for these functionsare also obtained.
Radius constants for functions associated with a limacon domain
조낙은,Anbhu Swaminathan,Lateef Ahmad Wani 대한수학회 2022 대한수학회지 Vol.59 No.2
Let $\mathcal{A}$ be the collection of analytic functions $f$ defined in $\mathbb{D}:=\left\{\xi\in\mathbb{C}:|\xi|<1\right\}$ such that $f(0)=f'(0)-1=0$. Using the concept of subordination ($\prec$), we define \begin{align*} \mathcal{S}^*_{\ell}:= \left\{f\in\mathcal{A}:\frac{\xi f'(\xi)}{f(\xi)}\prec\Phi_{\scriptscriptstyle{\ell}}(\xi)=1+\sqrt{2}\xi+\frac{\xi^2}{2},\;\xi\in\mathbb{D}\right\}, \end{align*} where the function $\Phi_{\scriptscriptstyle{\ell}}(\xi)$ maps $\mathbb{D}$ univalently onto the region $\Omega_{\ell}$ bounded by the limacon curve \begin{align*} \left(9u^2+9v^2-18u+5\right)^2-16\left(9u^2+9v^2-6u+1\right)=0. \end{align*} For $0<r<1$, let $\mathbb{D}_r:=\{\xi\in\mathbb{C}:|\xi|<r\}$ and $\mathcal{G}$ be some geometrically defined subfamily of $\mathcal{A}$. In this paper, we find the largest number $\rho\in(0,1)$ and some function $f_0\in\mathcal{G}$ such that for each $f\in\mathcal{G}$ \begin{align*} \mathcal{L}_f(\mathbb{D}_r)\subset\Omega_{\ell} ~ ~ \text{\ for every }~ 0<r\leq\rho, \end{align*} and \begin{align*} \mathcal{L}_{f_0}(\partial\mathbb{D}_\rho)\cap\partial\Omega_{\ell}\neq\emptyset, \end{align*} where the function $\mathcal{L}_f:\mathbb{D}\to\mathbb{C}$ is given by \begin{align*} \mathcal{L}_f(\xi):=\frac{\xi f'(\xi)}{f(\xi)}, \quad f\in\mathcal{A}. \end{align*} Moreover, certain graphical illustrations are provided in support of the results discussed in this paper.
曺洛殷 釜山水産大學校 1988 釜山水産大學 硏究報告 Vol.28 No.2
本 論文에서는 p-葉 α-볼록 函數들에 대하여 몇가지 性質들을 調査하였다.