• 호남수학학술지
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• 제23권1호
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• pp.41-50
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• 2001

This paper concerns with the subclass of normalized analytic function f in D = {z : |z| < 1}, namely a ${\delta}$-convex function in a sector. This subclass is denoted by ${\Delta}({\delta})$, where ${\delta}$ is a real positive. Given $0<{\beta}{\leq}1$ then for $z{\in}D$, the exact ${\alpha}({\beta},\;{\delta})$ is found such that $f{\in}{\Delta}({\delta})$ implies $f{\in}S^*({\beta})$, where $S^*({\beta})$ is starlike of order ${\beta}$ in a sector. This work is a more general version of the result of Nunokawa and Thomas [11].

• 대한수학회지
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• 제51권3호
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• pp.567-592
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• 2014

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notions of harmonic Alexander operator and harmonic Libera operator are introduced and their properties are investigated.

• 호남수학학술지
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• 제45권1호
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• pp.71-81
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• 2023

In this paper, we deal with some geometric properties including starlikeness and convexity of order 𝛽 of Ramanujan-type entire functions which are natural extensions of classical Ramanujan entire functions. In addition, we determine some conditions on the parameters such that the Ramanujan-type entire functions belong to the Hardy space and to the class of bounded analytic functions.

• Kyungpook Mathematical Journal
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• 제46권4호
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• pp.543-552
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• 2006

The purpose of the present paper is to introduce two novel subclasses $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$ and $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions with negative coefficients, involving Ruscheweyh derivative operator. The various results investigated in this paper include coefficient estimates, distortion inequalities, radii of close-to-convexity, starlikenes, and convexity for the functions belonging to the class $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$. These results are then appropriately applied to derive similar geometrical properties for the other class $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions. Relevant connections of these results with those in several earlier investigations are briefly indicated.

• 대한수학회논문집
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• 제38권4호
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• pp.1111-1126
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• 2023

In this paper, we define a new subclass of k-uniformly starlike functions of order γ (0 ≤ γ < 1) by using certain generalized q-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q-sufficient coefficient condition, q-Fekete-Szegö inequalities, q-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order γ by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.

• East Asian mathematical journal
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• 제24권4호
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• pp.347-358
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• 2008

In this paper we investigate integral means inequalities for the integral operators $Q_{\lambda}^{\mu}$ and $P_{\lambda}^{\mu}$ applied to suitably normalized analytic functions. Further, we obtain some neighborhood and inclusion properties for a class of functions $G{\alpha}({\phi}, {\psi})$ (defined below). Several corollaries exhibiting the applications of the main results are considered in the concluding section.

• 호남수학학술지
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• 제42권4호
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• pp.701-717
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• 2020

We introduced and studied a new class of harmonic univalent functions on unit disc 𝕌. Also we provided coefficient conditions, extreme points and convolution conditions for that class of harmonic univalent functions.

• Korean Journal of Mathematics
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• 제25권3호
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• pp.389-403
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• 2017

The purpose of the present paper is to introduce and study new subclasses of analytic functions which generalize the classes of Janowski functions with respect to k-symmetric points. We also study certain interesting properties like covering theorem, convolution condition, neighborhood results and argument theorem.

• 대한수학회지
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• 제58권5호
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• pp.1147-1180
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• 2021

By considering the polynomial function 𝜙_car(z) = 1 + z + z²/2, we define the class 𝓢^*_car consisting of normalized analytic functions f such that zf'/f is subordinate to 𝜙_car in the unit disk. The inclusion relations and various radii constants associated with the class 𝓢^*_car and its connection with several well-known subclasses of starlike functions is established. As an application, the obtained results are applied to derive the properties of the partial sums and convolution.

• 대한수학회논문집
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• 제35권3호
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• pp.867-877
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• 2020

The aim of this article is to make a connection between the Pascal distribution series and some subclasses of normalized analytic functions whose coefficients are probabilities of the Pascal distribution. To be more precise, we investigate such connections with the classes of analytic univalent functions with positive coefficients in the open unit disk 𝕌.