• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.395-410
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• 2015

For functions $f(z)=z+a_2z^2+a_3z^3+{\cdots}$ with ${\mid}a_2{\mid}=2b$, $b{\geq}0$, sharp radii of starlikeness of order ${\alpha}(0{\leq}{\alpha}<1)$, convexity of order ${\alpha}(0{\leq}{\alpha}<1)$, parabolic starlikeness and uniform convexity are derived when ${\mid}a_n{\mid}{\leq}M/n^2$ or ${\mid}a_n{\mid}{\leq}Mn^2$ (M>0). Radii constants in other instances are also obtained.

• Brain Tumor Research and Treatment
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• v.6 no.2
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• pp.97-100
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• 2018

Meningioma is relatively common, benign, and extra-axial tumor accounting for about 20% of primary brain and spinal cord tumors. The World Health Organization (WHO) classified these tumors into Grade I (benign), Grade II (atypical), and Grade III (anaplastic) meningioma. Grade I meningioma which is slowly growing tumor and have some rare subtypes. Among them, metaplastic subtype is defined as a tumor containing focal or widespread mesenchymal components including osseous, cartilaginous, lipomatous, myxoid or xanthomatous tissue, singly or in combinations. We report a rare metaplastic meningioma overspreading nearly whole cerebral convexity from main extra-axial tumor bulk in the parietal lobe.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.433-442
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• 2021

Let X and X^* be a Banach space and its dual, respectively, and let B(X) and S(X) be the unit ball and unit sphere of X, respectively. In this paper, we study the relation between Modulus of n-dimensional U-convexity in X^* and normal structure in X. Some new results about fixed points of nonexpansive mapping are obtained, and some existing results are improved. Among other results, we proved: if X is a Banach space with $U^n_{X^*}(n+1)>1-{\frac{1}{n+1}}$ where n ∈ ℕ, then X has weak normal structure.

• The korean journal of orthodontics
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• v.28 no.5 s.70
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• pp.751-761
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• 1998

The purpose of this study was to find the characteristics of lateral crphalogram of skeletal class III malocclusion patients to whom orthognathic surgery was essential. For this study 37 patients with skeletal class III and going to treat or be treated orthognathic surgery(age 7-17) were selected to experimental group and 56 people with normal occlusion (age 8-13) were selected to normal group and the two groups were evaluated and statistically analyzed and the results were as follows 1. In comparison of experimental group and normal group in prepubertal group, there were significant differences in ANS-U1/Me-L1, Mx. Length/Mn. Length, S-N/Go-Me, Wits, ANB, SN-Pog, IMPA, Facial Convexity, APDI (p<0.05) 2. In comparison of experimental group and normal group in pubertal group, there were significant differences in ANS-U1/Me-L1, S-Go/N-Me, Mx.Length/Mn.Length, S-N/Go-Me, Wits, Saddle Angle, SNB, ANB, SN-Pog, IMPA, Interincisal Angle, Facial Convexity, APDI (p<0.05) 3. Among items showing characteristics of skeletal class III malocclusion, there were no significant differences between prepubertal group and pubertal group in other items except Mx. Length/Mn. Length,APDI (p<0.05) 4. The significant correlationship was the highest between Saddle Angle and SNB, SN-Pog and SNB, ANB and Facial Convexity in experimental group

• Honam Mathematical Journal
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• v.38 no.3
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• pp.495-506
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• 2016

In this paper, we introduce and investigate a new subclass of meromorphic functions associated with a certain integral operator on Hilbert space. For this class, we obtain several properties like the coefficient inequality, extreme points, radii of close-to-convexity, starlikeness and meromorphically convexity and integral transformation. Further, it is shown that this class is closed under convex linear combination.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.513-527
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• 2015

In this paper, we first introduce and study new concepts of ($k_1,{\cdots},k_n$)-convexity and k-segment. Secondly, we shall discuss some properties of nonisotropically starlike domains in $\mathbb{R}^n$ with respect to the origin.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.335-341
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• 2008

In this paper, we use the convexity of distance function between geodesics in a singular Hadamard space to generalize Hadamard-Cartan theorem for 2-dimensional metric spaces. We also determine a neighborhood of a closed geodesic where no other closed geodesic exists in a complete space of nonpositive curvature.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.251-261
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• 2008

In this paper second order cone convex, second order cone pseudoconvex, second order strongly cone pseudoconvex and second order cone quasiconvex functions are introduced and their interrelations are discussed. Further a MondWeir Type second order dual is associated with the Vector Minimization Problem and the weak and strong duality theorems are established under these new generalized convexity assumptions.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.499-507
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• 2010

A new class of univalent holomorphic functions with fixed finitely many coefficients based on Generalized fractional derivative are introduced. Also some important properties of this class such as coefficient bounds, convex combination, extreme points, Radii of starlikeness and convexity are investigated.

• Journal of the Korean Statistical Society
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• v.1 no.1
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• pp.18-24
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• 1973

Study on convexity has been improved in many statistical fields, such as linear programming, stochastic inverntory problems and decision theory. In proof of main theorem in Section 3, M. Loeve already proved this theorem with the $r$-th absolute moments on page 160 in [1]. Main consideration is given to prove this theorem using convex theorems with the generalized $t$-th mean when some convex properties hold on a real linear vector space $R_N$, which satisfies all properties of finite dimensional Hilbert space. Throughout this paper $\b{x}_j, \b{y}_j$ where $j = 1,2,......,k,.....,N$, denotes the vectors on $R_N$, and $C_N$ also denotes a subspace of $R_N$.