• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.11 no.3
• /
• pp.37-41
• /
• 2007

The semi-convexity for planar shapes has been recently introduced in [2]. As a generalization of the convextiy, semi-convexity is closed under the Minkowski sum. But the definition of semi-convexity requires that the shape boundary should satifisfy a differentiability condition $C^{1:1}$, which means that it should be possible to take the normal vector field along the domain's extended boundary. In view of the fact that the semi-convextiy is a most natural generalization of the convexity in many respects, this is a severe restriction for the semi-convexity, since the convexity requires no such a priori differentiability condition. In this paper, we generalize the semi-convexity to the closure of the class of semi-convex $\mathcal{M}$-domains for any Minkowski class $\mathcal{M}$, and show that this generalized semi-convexity is also closed under Minkowski sum.

• East Asian mathematical journal
• /
• v.21 no.2
• /
• pp.219-231
• /
• 2005

This paper investigates some results (Theorems 2.1-2.3, below) concerning certain classes of analytic and univalent functions, involving the familiar fractional derivative operators. We state interesting consequences arising from the main results by mentioning the cases connected with the starlikeness, convexity, close-to-convexity and quasi-convexity of geometric function theory. Relevant connections with known results are also emphasized briefly.

• Journal of applied mathematics & informatics
• /
• v.28 no.5_6
• /
• pp.1507-1518
• /
• 2010

In this article some generalized refinements of some inequalities for real quasi-cinvex, convex, concave, s-convex, s-concave, and $\alpha$-star s-convex mappings are obtained.

• Journal of the Korean Mathematical Society
• /
• v.60 no.3
• /
• pp.503-520
• /
• 2023

In this paper, using the theory of majorization, we discuss the Schur m power convexity for L-conjugate means of n variables and the Schur convexity for weighted L-conjugate means of n variables. As applications, we get several inequalities of general mean satisfying Schur convexity, and a few comparative inequalities about n variables Gini mean are established.

• Journal of applied mathematics & informatics
• /
• v.28 no.5_6
• /
• pp.1419-1430
• /
• 2010

Since Goetschel and Voxman [5] proposed a linear order on fuzzy numbers, several authors studied the concept of semicontinuity and convexity of fuzzy mappings defined through the order. Since the order is only defined for fuzzy numbers on $\mathbb{R}$, it is natural to find a new order for normal fuzzy sets on $\mathbb{R}^n$ in order to study the concept of semicontinuity and convexity of fuzzy mappings on normal fuzzy sets. In this paper, we introduce a new order "${\preceq}_s$ for normal fuzzy sets on $\mathbb{R}^n$ with respect to the support function. We define the semicontinuity and convexity of fuzzy mappings with this order. Some issues which are related with semicontinuity and convexity of fuzzy mappings will be discussed.

• Communications of the Korean Mathematical Society
• /
• v.23 no.2
• /
• pp.251-256
• /
• 2008

In this paper, we introduce the concept of the semi-preconvex set on preconvexity spaces. We study some properties for the semi-preconvex set. Also we introduce the concepts of the sc-convex function and $s^*c$-convex function. Finally, we characterize sc-convex functions, $s^*$-convex functions and semi-preconvex sets by using the co-convexity hull and the convexity hull.

• Korean Journal of Mathematics
• /
• v.31 no.2
• /
• pp.161-180
• /
• 2023

In this article, we will utilize (α, m)-convexity to create a new form of Simpson-Newton inequalities in quantum calculus by using q_𝝔1-integral and q_𝝔1-derivative. Newly discovered inequalities can be transformed into quantum Newton and quantum Simpson for generalized convexity. Additionally, this article demonstrates how some recently created inequalities are simply the extensions of some previously existing inequalities. The main findings are generalizations of numerous results that already exist in the literature, and some fundamental inequalities, such as Hölder's and Power mean, have been used to acquire new bounds.

• Honam Mathematical Journal
• /
• v.42 no.2
• /
• pp.301-318
• /
• 2020

In this paper, we introduce and study the concept of hyperbolic type convexity functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for this class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is hyperbolic convexity. Moreover, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities.

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

• The korean journal of orthodontics
• /
• v.15 no.2
• /
• pp.175-195
• /
• 1985

Vertical and horizontal growth occur in the craniofacial complex which ensues continuous changes in facial morphology, until the end of active growth period. Longitudinal study for individual is essential, in the research on growth and development, however, the difficulties in obtaining long term subjects in Korea, the research has been limited. The author analyzed the cephalometric roentgenogrems of 43 boys and 47 girls taken from the ages 6 to 10. The subjects were divided into 3 groups according to SN-MP angle and 2 groups according to gonial angle. In this longitudinal study, 21 variables were measure 4. The obtained results were as follows: 1. SN-MP angle and genial angle had no significant changes in each group with age. 2. With age, facial convexity of hard tissue decreased in all groups, facial angle of hard tissue increased in low SN-MP angle group, but facial convexity of soft tissue had no significant changes in all groups with age. 3. In comparison of high SN-MP angle group and low SN-MP angle group, the former had greater facial convexity and smaller facial angle than the latter. 4. SN-MP angle and the ratio of posterior dental height to anterior dental height had reverse correlation in all groups. 5. High genial angle group revealed larger SN-MP angle, anterior dental height facial convexity, but smaller mandibular length, and the ratio of posterior dental height to anterior dental height compared with low genial angle group.