• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.771-778
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• 1999

In this paper, we obtain some geometric inequalities for mixed volumes of a convex body and its polar dual. We also develop a lower bound of the product of quermassintegral of a convex body and its polar dual and give a lower bound for the product of the dual quermassintegral of any index of centrally symmetric convex body and that of its polar dual.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.589-595
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• 2007

In this paper, we introduce the concepts of the convexity hull and co-convex sets on preconvexity spaces. We study some properties for the co-convexity hull and characterize c-convex functions and c-concave functions by using the co-convexity hull and the convexity hull.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.239-250
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• 2018

In this paper, we establish some new Newton's type integral inequalities for p-harmonic convex functions. Some special cases are also discussed as applications of our main results. Results obtained in this paper may be starting point for further research.

• Journal of the Chungcheong Mathematical Society
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• v.4 no.1
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• pp.55-59
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• 1991

We consider perturbation problems and Lagrangians for convex set function optimization problems. In particular, we prove that the Lagrangian $L({\Omega},y)$ is a convex set function in ${\Omega}$ for each y if the perturbation function is convex.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.537-549
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• 2022

In this paper, we consider a convex univalent function f_α,β which maps the open unit disc 𝕌 onto the vertical strip domain Ω_α,β = {w ∈ ℂ : α < ℜ < (w) < β} and introduce new subclasses of both close-to-convex and bi-close-to-convex functions with respect to an odd starlike function associated with Ω_α,β. Also, we investigate the Fekete-Szegö type coefficient bounds for functions belonging to these classes.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.107-114
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• 2018

We establish some new ostrowski type inequalities for MT-convex function including first order derivative via Niemann-Trouvaille fractional integral. It is interesting to mention that our results provide new estimates on these types of integral inequalities for MT-convex functions.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.359-376
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• 2020

The present research investigates the bounds of an integral operator for convex functions and a differentiable function f such that |f'| is convex. Further, these bounds of integral operators specifically produce estimations of various classical fractional and recently defined conformable integral operators. These results also contain bounds of Hadamard type for symmetric convex functions.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.653-665
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• 2020

In this paper, we establish new integral inequalities via Riemann-Liouville fractional integrals and Katugampola fractional integrals for the class of functions whose derivatives in absolute value are exponentially convex functions and exponentially s-convex functions in the second sense.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.1
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• pp.145-149
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• 2008

The similarity measure is constructed for non-convex fuzzy membership function using well known Hamming distance measure. Comparison with convex fuzzy membership function is carried out, furthermore characteristic analysis for non-convex function are also illustrated. Proposed similarity measure is proved and the usefulness is verified through example. In example, usefulness of proposed similarity is pointed out.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.379-390
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• 2005

In this paper, optimality conditions for multiobjective programming problems having F-convex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function. Furthermore, an F-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of a saddle point are given.