• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.671-686
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• 2012

This paper mainly deals with the tilted Carath$\acute{e}$odory class by angle ${\lambda}$ ${\in}$ ($-{\pi}/2$, ${\pi}/2$), denoted by $P{\lambda}$) an element of which maps the unit disc into the tilted right half-plane {<${\omega}$ : Re $e^{i{\lambda}}{\omega}$ > 0}. Firstly we will characterize $P{\lambda}$ from different aspects, for example by subordination and convolution. Then various estimates of functionals over $P{\lambda}$ are deduced by considering these over the extreme points of $P{\lambda}$ or the knowledge of functional analysis. Finally some subsets of analytic functions related to $P{\lambda}$ including close-to-convex functions with argument ${\lambda}$, ${\lambda}$-spirallike functions and analytic functions whose derivative is in $P{\lambda}$ are also considered as applications.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.953-967
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• 2015

In this article, by making use of a linear multiplier fractional differential operator $D^{{\delta},m}_{\lambda}$, we introduce a new subclass of spiral-like functions. The main object is to provide some subordination results for functions in this class. We also find sufficient conditions for a function to be in the class and derive Fekete-$Szeg{\ddot{o}}$ inequalities.

• The Pure and Applied Mathematics
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• v.3 no.2
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• pp.103-111
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• 1996

Let $f(z)=z＋\alpha_2 z^2$＋…＋ \alpha_{n}z^n$＋… be regular and univalent in $\Delta$ = {z : │z│＜1}. In this paper, using the proper subordinate functions, we investigate the some relations between subordinations and conditions of functions belonging to subclasses of univalent functions.

• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.1121-1136
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• 2024

In this paper, by using a technique of the first-order differential subordination, we find several sufficient conditions for the tilted Carathéodory function of order β and angle α (α ∈ (-π/2, π/2) and β ∈ [0, cos α)), which maps the unit disk 𝔻 into the region {w ∈ ℂ : Re{e^iαw} > β}. Using these conditions, we also derive conditions for an analytic function that maps 𝔻 into a sector defined by {w ∈ ℂ : | arg(w - γ)| < (π/2)δ}, where γ ∈ [0, 1) and δ ∈ (0, 1]. The results obtained here will be applied to find some conditions for spirallike functions and strongly starlike functions in 𝔻.

• Communications of the Korean Mathematical Society
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• v.8 no.4
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• pp.603-615
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• 1993

• Kyungpook Mathematical Journal
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• v.51 no.4
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• pp.411-417
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• 2011

In the present paper, we are concerned with subordination problems related to ${\lambda}$-Robertson function. The radii of ${\lambda}$-spirallikeness and starlikeness of ${\lambda}$-Robert function are also determined.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1641-1665
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• 2017

The paper considers p-valent functions in the open unit disk. We study the integral means along with the area integral problems for functions belonging to a family of p-valent functions.