• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.21-22
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• 2008

Fuzzy entropy is designed for non-convex fuzzy membership function using well known Hamming distance measure. Design procedure of convex fuzzy membership function is represented through distance measure, furthermore characteristic analysis for non-convex function are also illustrated. Proof of proposed fuzzy entropy is discussed, and entropy computation is illustrated.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.37-40
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• 2002

In this paper, we introduce the concepts of m-convex and pseudo-m-convex for fuzzy mappings of one variable on the notion of differentiability proposed by Goeschel and Voxman, and investigate the relationship between m-convex fuzzy mappings and pesudo-m-convex fuzzy mappings.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.845-855
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• 2016

We introduce the proximal point algorithm in a p-uniformly convex metric space. We first introduce the notion of p-resolvent map in a p-uniformly convex metric space as a generalization of the Moreau-Yosida resolvent in a CAT(0)-space, and then we secondly prove the convergence of the proximal point algorithm by the p-resolvent map in a p-uniformly convex metric space.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.623-629
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• 2005

Inclusion relations under certain integral operators are proved for k-uniformly starlike functions. These results are also extended to k-uniformly convex, close-to-convex, and quasi-convex functions

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.87-93
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• 1998

Mejia and Minda proved that if a hyperbolic simply connected region $\Omega$ is k-convex, then (equation omitted), $z \in \Omega$. We show that this inequality actually characterizes k-convex regions.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.975-981
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• 1996

Let $D \subset C^2$ be a bounded convex domain with real analytic boundary. We get some Lipschitz regularity of the Cauchy transform on the convex domain D.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.665-669
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• 2002

In this paper, we study averaging properties in Banach space. We prove that the convex block Banach-Saks property is equivalent to the reflexivity in a Banach space. And we show that a weakly compact operator is a convex block Banach-Saks operator.

• 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.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.155-171
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• 2018

Some weighted integral inequalities of Hermite-Hadamard type for GG-convex functions defined on positive intervals are given. Applications for special means are also provided.