• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.1
• /
• pp.29-35
• /
• 2016

In this paper, we consider a convex optimization problem with a convex integrable objective function and a geometric constraint set. We characterize the solution set of the problem when we know its one solution.

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

• Korean Journal of Mathematics
• /
• v.28 no.4
• /
• pp.955-971
• /
• 2020

In this study, some new inequalities of Hermite-Hadamard type for convex and co-ordinated convex functions via Riemann-Liouville fractional integrals are derived. It is also shown that the results obtained in this paper are the extension of some earlier ones.

• Journal of applied mathematics & informatics
• /
• v.40 no.5_6
• /
• pp.1021-1034
• /
• 2022

In this article, authors derived Petrović's type inequalities for a class of functions, namely, called exponentially h-convex functions. Also, the associated results for coordinates has been derived by defining exponentially h-convex functions on coordinates.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.2
• /
• pp.197-206
• /
• 2010

We study the restriction estimate of Fourier transform to arbitrary convex curves in $R^2$ with no regularity assumption. Assuming that the convex curve has the lower bound of curvatures, we extend the restriction results from smooth convex curves to arbitrary convex curves. Our work has been motivated by the lecture notes of Terence Tao. The bilinear approach and geometric observations play an important role.

• Proceedings of the Korean Society of Computer Information Conference
• /
• 2020.07a
• /
• pp.83-84
• /
• 2020

Sum Utility를 최적화하는 Convex Optimization Algorithm을 제안한다. 일반적으로, Sum Utility 최적화 문제는 Non Convex Optimization Problem이다. 하지만, '상대간섭'과 '간섭주요화'를 활용하여 Non Convex Optimization Problem이 간섭구간에 따라 Convex Optimization으로 해결할 수 있음을 확인하였다. 특히, 유틸리티 함수는 상대간섭 0.1 이하에서는 오목함수임을 확인하였다. 실험결과 상대간섭이 작아질수록 제안하는 알고리즘에 의한 Sum Utility는 증가함을 확인하였다.

• East Asian mathematical journal
• /
• v.19 no.2
• /
• pp.207-212
• /
• 2003

Some new characterization of best approximants from level sets of convex functions in normed linear spaces in terms of norm derivatives are given.

• Journal of IKEEE
• /
• v.17 no.1
• /
• pp.29-35
• /
• 2013

In this paper, we suggest an improved Convex Hull algorithm considering sort in plane point set. This algorithm has low computational complexity since processing data are reduced by characteristic of extreme points. Also it obtains a complete convex set with just one processing using an convex vertex discrimination criterion. Initially it requires sorting of point set. However we can't quickly sort because of its heavy operations. This problem was solved by replacing value and index. We measure the execution time of algorithms by generating a random set of points. The results of the experiment show that it is about 2 times faster than the existing algorithm.

• Journal of applied mathematics & informatics
• /
• v.41 no.5
• /
• pp.963-972
• /
• 2023

In this paper, geometrically convex and s-convex functions in third and fourth sense are merged to form (g, s)-convex function. Characterizations of (g, s)-convex function, algebraic and functional properties are presented. In addition, novel functions based on the integral of (g, s)-convex functions in the third sense are created, and inequality relations for these functions are explored and examined under particular conditions. Further, there are also some relationships between (g, s)-convex function and previously defined functions. The (g, s)-convex function and its derivatives will then be used to extend the well-known H-H and Fejer's type inequalities. In order to obtain the previously mentioned conclusions, several special cases from previous literature for extended H-H and Fejer's inequalities are also investigated. The relation between the average (mean) values and newly created H-H and Fejer's inequalities are also examined.

• Journal of the Korea Society of Computer and Information
• /
• v.16 no.3
• /
• pp.99-107
• /
• 2011

The feature extraction of asterias amurensis by using patterns is difficult to extract all the concave and convex features of asterias amurensis nor classify concave and convex. Concave and convex as important structural features of asterias amurensis are the features which should be found and the classification of concave and convex is also necessary for the recognition of asterias amurensis later. Accordingly, this study suggests the technique to extract the features of concave and convex, the main features of asterias amurensis. This technique classifies the concave and convex features by using the multi-directional linear scanning and form the candidate groups of the concave and convex feature points and decide the feature points of the candidate groups and apply convex hull algorithm to the extracted feature points. The suggested technique efficiently extracts the concave and convex features, the main features of asterias amurensis by dividing them. Accordingly, it is expected to contribute to the studies on the recognition of asterias amurensis in the future.