• East Asian mathematical journal
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• v.26 no.1
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• pp.49-58
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• 2010

In this paper, we consider and study a new class of generalized vector quasi-variational type inequalities and obtain some existence theorems for both under compact and noncompact assumptions in topological vector spaces without using monotonicity. For the noncompact case, we use the concept of escaping sequences.

• ETRI Journal
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• v.18 no.3
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• pp.207-213
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• 1996

This paper proposes a new nonparametric test for testing the null hypothesis that the MRL is constant against the alternative hypothesis that the MRL is decreasing (increasing) for ramdomly censored data. The proposed test statistic is a L-statistic, and we use L-statistic theory to establish its asymptotic normality of the test statistic. We discuss the efficiency loss due to censoring and also calculate the asymptotic relative efficiencies of our test statistic with respect to the Chen, Hollander and Langberg's test for several alternatives.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.165-172
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• 2003

In this paper, we introduce the concept of well-posedness for general variational inequalities and obtain some results under pseudomonotonicity. It is well known that monotonicity implies pseudomonotonicity, but the converse is not true. In this respect, our results represent an improvement and refinement of the previous known results. Since the general variational inequalities include (quasi) variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.183-191
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• 2007

In this paper, we introduce and study a new class of equilibrium problems, known as regularized mixed quasi equilibrium problems. We use the auxiliary principle technique to suggest and analyze some iterative schemes for regularized equilibrium problems. We prove that the convergence of these iterative methods requires either pseudomonotonicity or partially relaxed strongly monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving equilibrium problems and variational inequalities involving the convex sets.

• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.649-652
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• 2000

Beyond free choice net system this paper presents some liveness knowledge in asymmetric net system including necessary and sufficient condition for an asymmetric net system being live and having liveness monotonicity, and an algorithm, polynomial time complexity, for such deciding. Also two conjectures about system livenss are in the contribution.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.479-495
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• 2013

Taking the weighted geometric mean [11] on the cone of positive definite matrix, we propose an iterative mean algorithm involving weighted arithmetic and geometric means of $n$-positive definite matrices which is a weighted version of Carlson mean presented by Lee and Lim [13]. We show that each sequence of the weigthed Carlson iterative mean algorithm has a common limit and the common limit of satisfies weighted multidimensional versions of all properties like permutation symmetry, concavity, monotonicity, homogeneity, congruence invariancy, duality, mean inequalities.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.749-754
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• 1999

The cost is known to be proportional to the size of sample. We consider a cost function of the form Cost=c1np+c2npmq where c1, c2 p, and q are all positive constants. This cost function is to be used in finding an optimal allocation in two-stage cluster sampling. The optimal allocations of n and m gives the properties of uniqueness under some conditions and of monotonicity with p>0 when q=1.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.737-743
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• 2003

The purpose of this paper is to consider some existence results for vector nonlinear inequalities without any monotonicity assumption. As consequences of our main result, we give some existence results for vector equilibrium problem, vector variational-like inequality problem and vector variational inequality problems as special cases.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.373-383
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• 2010

In this paper, we prove that $(\Gamma(x))^{\frac{1}{x-1}}$ is geometrically convex on (0, $\infty$). As its applications, we obtain some new estimates for $\frac{[\Gamma(x+1)]^{\frac{1}{x}}} {[\Gamma(y+1)]^{\frac{1}{y}}}$.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1133-1148
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• 2016

In this paper, we first discuss a representation of solutions to the initial value problem and the initial-boundary value problem for discrete evolution equations $${\sum\limits^l_{n=0}}c_n{\partial}^n_tu(x,t)-{\rho}(x){\Delta}_{\omega}u(x,t)=H(x,t)$$, defined on networks, i.e. on weighted graphs. Secondly, we show that the weight of each link of networks can be uniquely identified by using their Dirichlet data and Neumann data on the boundary, under a monotonicity condition on their weights.