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RISS 인기검색어
- 검색키워드
- 저자 : Anbhu Swaminathan (검색결과 4 건)
- 무료
- 기관 내 무료
- 유료
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Sufficient conditions and radii problems for a starlike class involving a differential inequality
Anbhu Swaminathan,Lateef Ahmad Wani 대한수학회 2020 대한수학회보 Vol.57 No.6
Let $\mathcal{A}_n$ be the class of analytic functions $f(z)$ of the form $f(z)=z+\sum_{k=n+1}^\infty a_kz^k$, $n\in\mathbb{N}$ defined on the open unit disk $\mathbb{D}$, and let \begin{align*} \Omega_n:=\left\{f\in\mathcal{A}_n:\left|zf'(z)-f(z)\right|<\frac{1}{2},\; z\in\mathbb{D}\right\}. \end{align*} In this paper, we make use of differential subordination technique to obtain sufficient conditions for the class $\Omega_n$. Writing $\Omega:=\Omega_1$, we obtain inclusion properties of $\Omega$ with respect to functions which map $\mathbb{D}$ onto certain parabolic regions and as a consequence, establish a relation connecting the parabolic starlike class $\mathcal{S}_P$ and the uniformly starlike $UST$. Various radius problems for the class $\Omega$ are considered and the sharpness of the radii estimates is obtained analytically besides graphical illustrations.
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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.
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MONOTONICITY PROPERTIES OF THE BESSEL-STRUVE KERNEL
Baricz, Arpad,Mondal, Saiful R.,Swaminathan, Anbhu Korean Mathematical Society 2016 대한수학회보 Vol.53 No.6
In this paper our aim is to study the classical Bessel-Struve kernel. Monotonicity and log-convexity properties for the Bessel-Struve kernel, and the ratio of the Bessel-Struve kernel and the Kummer confluent hypergeometric function are investigated. Moreover, lower and upper bounds are given for the Bessel-Struve kernel in terms of the exponential function and some $Tur{\acute{a}}n$ type inequalities are deduced.
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Monotonicity properties of the Bessel-Struve kernel
\'Arp\'ad Baricz,Saiful R. Mondal,Anbhu Swaminathan 대한수학회 2016 대한수학회보 Vol.53 No.6
In this paper our aim is to study the classical Bessel-Struve kernel. Monotonicity and log-convexity properties for the Bessel-Struve kernel, and the ratio of the Bessel-Struve kernel and the Kummer confluent hypergeometric function are investigated. Moreover, lower and upper bounds are given for the Bessel-Struve kernel in terms of the exponential function and some Tur\'an type inequalities are deduced.
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