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395 results on '"Cho, Nak Eun"'

2. New Criteria for Functions in a Class of Meromorphically Strongly Starlike Functions

Author

Cho Nak Eun, Kim Inhwa, and Srivastava H. M.

Subjects
analytic functions, univalent functions, starlike functions, meromorphic functions, principle of subordination, argument estimates, strongly starlike functions, meromorphically strongly starlike functions, primary 30c45, 30c80, secondary 30a20, 30a40, Mathematics, QA1-939
Abstract

The authors propose to investigate some new criteria for a certain class of meromorphically strongly starlike functions in the punctured open unit disk. Some intriguing applications that arise as special cases of the main results, which are presented in this study, are also considered.

Published
2024
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3. Sufficient conditions for strong starlikeness

Author

Sharma, Kanika, Cho, Nak Eun, and Ravichandran, V.

Subjects
Mathematics - Complex Variables, 30C80, 30C45
Abstract

Let $p$ be an analytic function defined on the open unit disc $\mathbb{D}$ with $p(0)=1$ and $0< \alpha \leq 1$. The conditions on complex valued functions $C$, $D$ and $E$ are obtained for $p$ to be subordinate to $((1+z)/(1-z))^{\alpha}$ when $C(z) z^{2}p''(z)+D(z)zp'(z) + E(z)p(z)=0$. Sufficient conditions for confluent (Kummer) hypergeometric function and generalized and normalized Bessel function of the first kind of complex order to be subordinate to $((1+z)/(1-z))^{\alpha}$ are obtained as applications. The conditions on $\alpha$ and $\beta$ are derived for $p$ to be subordinate to $((1+z)/(1-z))^{\alpha}$ when $1+\beta zp'(z)/p^{n}(z)$ with $n=1,2$ is subordinate to $1+4z/3+2z^{2}/3=:\varphi_{CAR}(z)$. Similar problems were investigated for $\RE p(z)>0$ when the functions $p(z)+\beta zp'(z)/p^{n}(z)$ with $n=0,2$ is subordinate to $\varphi_{CAR}(z)$. The condition on $\beta$ is determined for $p$ to be subordinate to $((1+z)/(1-z))^{\alpha}$ when $p(z)+\beta zp'(z)/p^{n}(z)$ with $n=0,1,2$ is subordinate to $((1+z)/(1-z))^{\alpha}$.

Published
2020

18. Coefficient, Distortion and Growth Inequalities for Certain Close-to-Convex Functions

Author

Cho, Nak Eun, Kwon, Oh Sang, and Ravichandran, V.

Subjects
Mathematics - Complex Variables, 30C45
Abstract

In the present investigation, certain subclasses of close-to-convex functions are investigated. In particular, we obtain an estimate for the Fekete-Szeg\"o functional for functions belonging to the class, distortion, growth estimates and covering theorems.

Published
2011
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19. A first-order differential double subordination with applications

Author

Ali, Rosihan M., Cho, Nak Eun, Kwon, Oh Sang, and Ravichandran, V.

Subjects
Mathematics - Complex Variables, 30C45
Abstract

Let $q_1$ and $q_2$ belong to a certain class of normalized analytic univalent functions in the open unit disk of the complex plane. Sufficient conditions are obtained for normalized analytic functions $p$ to satisfy the double subordination chain $q_1(z)\prec p(z)\prec q_2(z)$. The differential sandwich-type result obtained is applied to normalized univalent functions and to $\Phi$-like functions.

Published
2011
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30. First-order differential subordinations associated with Carathéodory functions.

Author

Kim, Inhwa, Sim, Young Jae, and Cho, Nak Eun

Subjects
GEOMETRIC function theory, UNIVALENT functions, ANALYTIC functions, STAR-like functions
Abstract

In the present paper, we investigated some conditions to be in the class of Carathéodory functions by using the concept of the first-order differential subordinations. Moreover, various interesting special cases were considered in the geometric function theory as applications of main results presented here. [ABSTRACT FROM AUTHOR]

Published
2024
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31. Initial Coefficient Bounds for Certain New Subclasses of bi-Bazilevič Functions and Exponentially bi-Convex Functions with Bounded Boundary Rotation.

Author

Sharma, Prathviraj, Sivasubramanian, Srikandan, and Cho, Nak Eun

Subjects
ROTATIONAL motion, UNIVALENT functions
Abstract

The objective of the present article is to introduce new subclasses of bi-Bazilevič functions, bi-quasi-convex functions and α -exponentially bi-convex functions involving functions with bounded boundary rotation of order ν. For the above-said newly defined classes, we obtain first two initial coefficient bounds. In addition, the familiar Fekete–Szegö coefficient inequality is too found for the newly introduced subclasses of bi-univalent functions. Apart from the new findings that are obtained, it also improves the prior estimates that are presented already in the literature. [ABSTRACT FROM AUTHOR]

Published
2024
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33. Convex combination of analytic functions

Author

Cho Nak Eun, Jain Naveen Kumar, and Ravichandran V.

Subjects
convex function, starlike function, close-to-convex function, lemniscate of bernoulli, radius of starlikeness, convolution, convex combination, 30c80, 30c45, Mathematics, QA1-939
Abstract

Radii of convexity, starlikeness, lemniscate starlikeness and close-to-convexity are determined for the convex combination of the identity map and a normalized convex function F given by f(z) = α z+(1−α)F(z).

Published
2017
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49. First-Order Differential Subordinations and Their Applications.

Author

Ebadian, Ali, Aghalary, Rasoul, Shams, S., Cho, Nak Eun, and Alavi, R.

Subjects
CONVEX functions, ANALYTIC functions, STAR-like functions
Abstract

In this paper, we consider some relations related to the representations of starlike and convex functions, and obtain some sufficient conditions for starlike and convex functions by using the theory of differential subordination. Actually, we generalize a result by Suffridge for analytic functions with missing coefficients and then we apply that generalization for obtaining the different methods to the implications of starlike or convex functions. Our results generalize and improve the previous results in the literature. [ABSTRACT FROM AUTHOR]

Published
2023
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