• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.199-202
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• 2007

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 the Korean Mathematical Society
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• v.50 no.5
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• pp.933-944
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• 2013

Based on the four kinds of theoretical definitions of the continuous module homomorphism between random locally convex modules, we first show that among them there are only two essentially. Further, we prove that such two are identical if the family of $L^0$-seminorms for the former random locally convex module has the countable concatenation property, meantime we also provide a counterexample which shows that it is necessary to require the countable concatenation property.

• 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.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.843-860
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• 2019

In the article, we present several new Hermite-Hadamard and Hermite-Hadamard-Fejér type inequalities for the exponentially (ħ, m)-convex functions via an extended generalized Mittag-Leffler function. As applications, some variants for certain typ e of fractional integral operators are established and some remarkable special cases of our results are also have been obtained.

• The Pure and Applied Mathematics
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• v.20 no.1
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• pp.51-57
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• 2013

In this paper, we introduce asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces and consider approximating common fixed points of a sequence of asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.39-46
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• 2017

In this paper, we propose a new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex cone metric spaces. Then we show that our iteration converges to a common fixed point of this class of mappings under suitable conditions. Our result generalizes the corresponding result of Lee [5] from the closed convex subset of a convex cone metric space to whole space.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.105-110
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• 2010

In this paper, we introduce the concept of $\beta$-preconvex sets on preconvexity spaces. We study some properties for $\beta$-preconvex sets by using the co-convexity hull and the convexity hull. Also we introduce and study the concepts of ${\beta}c$-convex function and $\beta^*c$-convex function.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.369-374
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• 2016

In this paper, we study the hereditary convex radius of convex harmonic mapping $f(z)=f_1(z)+{\bar{f_x(z)}}$ under the integral operator $I_f(z)={\int_{o}^{z}}{\frac{f_1(u)}{u}}du+{\bar{{\int_{o}^{z}}{\frac{f_x(u)}{u}}}}$ and obtain the sharp constant ${\frac{{\sqrt[4]{6}}-{\sqrt[]{15}}}{9}}$, which generalized the result corresponding to the class of analytic functions given by Nash.

• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.371-378
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• 2010

In this paper, we establish new inequalities of Ostrowski's type for functions whose derivatives in absolute value are (${\alpha}$, m)-convex.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.4-9
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• 2009

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.