• 품질경영학회지
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• 제42권4호
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• pp.685-700
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• 2014

Purpose: The purpose of this paper is to develop a systematic weighting procedure based on process capability indices method applying weighted mean squared error minimization (WMSE) approach to dual response surface optimization. Methods: The proposed procedure consists of 5 steps. Step 1 is to prepare the alternative vectors. Step 2 is to rank the vectors based on process capability indices in a pairwise manner. Step 3 is to transform the pairwise rankings into the inequalities between the corresponding WMSE values. Step 4 is to obtain the weight value by calculating the inequalities. Or, step 5 is to obtain the weight value by minimizing the total violation amount, in case there is no weight value in step 4. Results: The typical 4 process capability indices, namely, $C_p$, $C_{pk}$, $C_{pm}$, $C_{pmk}$ are utilized for the proposed procedure. Conclusion: The proposed procedure can provide a weight value in WMSE based on the objective quality performance criteria, not on the decision maker's subjective judgments or experiences.

• Communications for Statistical Applications and Methods
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• 제21권3호
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• pp.201-212
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• 2014

We provide a simple basic method to find bounds for higher order moments of unimodal distributions in terms of lower order moments when the random variable takes value in a given finite real interval. The bounds for moments in terms of the geometric mean of the distribution are also derived. Both continuous and discrete cases are considered. The bounds for the ratio and difference of moments are obtained. The special cases provide refinements of several well-known inequalities, such as Kantorovich inequality and Krasnosel'skii and Krein inequality.

• Kyungpook Mathematical Journal
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• 제52권4호
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• pp.495-511
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• 2012

In this paper, we prove some inequalities in terms of G$\hat{a}$teaux derivatives for convex functions defined on linear spaces and also give improvement of Jensen's inequality. Furthermore, we give applications for norms, mean $f$-deviations and $f$-divergence measures.

• 대한수학회지
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• 제53권4호
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• pp.769-780
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• 2016

In this paper, we first prove some Liouville type theorems for elliptic inequalities on weighted manifolds which support a weighted Sobolev-type inequality. Secondly, applying the Liouville type theorems to self-shrinkers, we obtain some global rigidity theorems.

• 대한수학회논문집
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• 제38권1호
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• pp.153-161
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• 2023

In this paper, we introduce a new concept for bivariate means and we study its properties. Application of this concept for mean-inequalities is also discussed. Open problems are derived as well.

• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.521-529
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• 2014

In this paper we derive some optimal convex combination bounds related to arithmetic mean. We find the greatest values ${\alpha}_1$ and ${\alpha}_2$ and the least values ${\beta}_1$ and ${\beta}_2$ such that the double inequalities $${\alpha}_1T(a,b)+(1-{\alpha}_1)H(a,b)<A(a,b)<{\beta}_1T(a,b)+(1-{\beta}_1)H(a,b)$$ and $${\alpha}_2T(a,b)+(1-{\alpha}_2)G(a,b)<A(a,b)<{\beta}_2T(a,b)+(1-{\beta}_2)G(a,b)$$ holds for all a,b > 0 with $a{\neq}b$. Here T(a,b), H(a,b), A(a,b) and G(a,b) denote the second Seiffert, harmonic, arithmetic and geometric means of two positive numbers a and b, respectively.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.227-245
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• 2011

In this paper, we introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a ${\beta}$inverse-strongly monotone mapping and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Ces$\`{a}$ro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang [A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mapping, Nonlinear Analysis: Hybrid Systems, 3(2009), 475-86], Peng and Yao [Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems, Mathematical and Computer Modelling, 49(2009), 1816-828], Shimizu and Takahashi [Strong convergence to common fixed points of families of nonexpansive mappings, Journal of Mathematical Analysis and Applications, 211(1) (1997), 71-83] and some authors.

• 한국경영과학회지
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• 제22권3호
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• pp.11-22
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• 1997

The aim of this paper is to develop the B & B type algorithms for globally minimizing concave function under 0-1 knapsack constraint. The linear convex envelope underestimating the concave object function is introduced for the bounding operations which locate the vertices of the solution set. And the simplex containing the solution set is sequentially partitioned into the subsimplices over which the convex envelopes are calculated in the candidate problems. The adoption of cutting plane method enhances the efficiency of the algorithm. These mean valid inequalities with respect to the integer solution which eliminate the nonintegral points before the bounding operation. The implementations are effectively concretized in connection with the branching stategys.

• 대한수학회논문집
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• 제28권2호
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• pp.231-241
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• 2013

On the framework of the 2-adic group $\mathcal{Z}_2$, we study a Sobolev-like inequality where we estimate the $L^2$ norm by a geometric mean of the BV norm and the $\dot{B}_{\infty}^{-1,{\infty}}$ norm. We first show, using the special topological properties of the $p$-adic groups, that the set of functions of bounded variations BV can be identified to the Besov space ˙$\dot{B}_1^{1,{\infty}}$. This identification lead us to the construction of a counterexample to the improved Sobolev inequality.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.775-784
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• 2021

For the polynomial P(z) of degree n and having all its zeros in |z| ≤ k, k ≥ 1, Jain [6] proved that $${{\max\limits_{{\mid}z{\mid}=1}}\;{\mid}P^{\prime}(z){\mid}{\geq}n\;{\frac{{\mid}c_0{\mid}+{\mid}c_n{\mid}k^{n+1}}{{\mid}c_0{\mid}(1+k^{n+1})+{\mid}c_n{\mid}(k^{n+1}+k^{2n})}\;{\max\limits_{{\mid}z{\mid}=1}}\;{\mid}P(z){\mid}$$. In this paper, we extend above inequality to its integral analogous and there by obtain more results which extended the already proved results to integral analogous.