• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.449-461
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• 2001

The purpose of this paper is to study several geometric properties for the new class $G_{\kappa}(\beta)$ including geometric interpretation, coefficient estimates, radius of convexity, distortion property and covering theorem.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1395-1408
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• 2010

In this paper, a pair of Wolfe type second-order nondifferentiable multiobjective symmetric dual program over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under second-order (F, $\alpha$, $\rho$, d)-convexity assumptions. An illustration is given to show that second-order (F, $\alpha$, $\rho$, d)-convex functions are generalization of second-order F-convex functions. Several known results including many recent works are obtained as special cases.

• The Pure and Applied Mathematics
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• v.15 no.4
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• pp.387-392
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• 2008

In this note, an alternative proof and extensions are provided for the following conclusions in [6, Theorem 1 and Theorem 3]: The functions $\frac1{x^2}-\frac{e^{-x}}{(1-e^{-x})^2}\;and\;\frac1{t}-\frac1{e^t-1}$ are decreasing in (0, ${\infty}$) and the function $\frac{t}{e^{at}-e^{(a-1)t}}$ for a $a{\in}\mathbb{R}\;and\;t\;{\in}\;(0,\;{\infty})$ is logarithmically concave.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.313-334
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• 2024

In the current study, our aim is to define new generalized extended beta and hypergeometric types of functions. Next, we methodically determine several integral representations, Mellin transforms, summation formulas, and recurrence relations. Moreover, we provide log-convexity, Turán type inequality for the generalized extended beta function and differentiation formulas, transformation formulas, differential and difference relations for the generalized extended hypergeometric type functions. Also, we additionally suggest a generating function. Further, we provide the generalized extended beta distribution by making use of the generalized extended beta function as an application to statistics and obtaining variance, coefficient of variation, moment generating function, characteristic function, cumulative distribution function, and cumulative distribution function's complement.

• The korean journal of orthodontics
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• v.31 no.5 s.88
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• pp.479-487
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• 2001

The perception of facial esthetics is critically important to orthodontists. A viewpoint to facial esthetics is influenced by various factors and dependent on the perception of observer. The purpose of this study was to examine the differences regarding esthetic viewpoints among orthodontists, to identify attractive profiles preferred to orthodontists and to present the characteristic aspects of attractive profiles upon the degree of facial convexity. 35 persons whose faces were judged as attractive one by S orthodontists were selected out of 133 young Korean women. Soft tissue profiles Identified as a good-profile group were measured and analyzed. And then according to the facial convexity, good-profile group was subdivided to convex (G-Sn-Pg$9^{\circ}$) and straight (G-Sn-Pg<$9^{\circ}$) groups for the purpose of this study. There were statistically no significant differences regarding esthetic viewpoints among S orthodontists(p<0.05), even if there exists prevailing concept that the standard for facial esthetics is substantially subjective. N-Pg-Sn and N-Pg-Pn, measured for determining anteroposterior relationship of midfacial convexity, showed significant differences statistically between 2 subgroups (P

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.285-291
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• 1997

In this paper, we obtain an abstract formulation of a fixed point theorem for nonexpansive mappings. Our theorem is a non-metric version of Kirk's original theorem.

• Korean Journal of Mathematics
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• v.5 no.1
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• pp.83-89
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• 1997

In this paper we generalize the concept of normality for the problem involving set functions in a view of Jahn. The main result is that the problem with Slater's constraint qualification is normal and stable.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.33-44
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• 2017

We review weighted power means of positive real numbers and see their properties including the convexity and concavity for weights. We study the mixed power means of positive real numbers related to majorization of weights, which gives us an extension of Muirhead's inequality. Furthermore, we generalize Holland's conjecture to the power means.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.593-602
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• 2021

In this paper, the concept of s-convex function in the third sense is given. Then fundamental characterizations and some basic algebraic properties of s-convex function in the third sense are presented. Also, the relations between the third sense s-convex functions according to the different values of s are examined.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.89-99
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• 2019

The Steffensen's Inequality was discovered in 1918 by Johan Frederic Steffensen (1873-1961). This inequality is very popular in the research environment and attracted the attention of many people working in similar area. Various extensions and generalisations have been provided concerning the inequality. This paper presents some further refinements of the Steffensen's Inequality on Time scales using methods of convexity, differentiability and monotonicity.