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A note on a regularized gap function of QVI in Banach spaces
금상호 충청수학회 2014 충청수학회지 Vol.27 No.2
Recently, Taji [7] and Harms et al. [4] studied the regularized gap function of QVI analogous to that of VI by Fukushima [2]. Discussions are made in a finite dimensional Euclidean space. In this note, an infinite dimensional generalization is considered in the framework of a reflexive Banach space. To do so, we introduce an extended quasi-variational inequality problem (in short, EQVI) and a generalized regularized gap function of EQVI. Then we investigate some basic properties of it. Our results may be regarded as an infinite dimensionalextension of corresponding results due to Taji [7].
A characterization of solutions of affine variational inequality defined by second-order cone
금상호 충청수학회 2007 충청수학회지 Vol.20 No.3
A variational inequality defined by the second-order cone is considered, and it is shown that a necessary and sufficient condition for a solution of the variational inequality holds under some regularity condition.
A Remark on a Combined Relaxation Method to Variational Inequality
금상호 충청수학회 2008 충청수학회지 Vol.21 No.3
In this paper, we propose a simple iterative method based on the combined relaxation approach for a nonlinear variational inequality problem, which is equivalent to the usual variational inequality with a single valued cost mapping. We establish a convergence result for our method under mild assumptions.
A remark on multi-valued generalized system
금상호 충청수학회 2011 충청수학회지 Vol.24 No.2
Recently, Kazmi and Khan [7] introduced a kind of equilibrium problem called generalized system (GS) with a single-valued bi-operator F. In this note, we aim at an extension of (GS) due to Kazmi and Khan [7] into a multi-valued circumstance. We consider a fairly general problem called the multi-valued quasi-generalized system (in short, MQGS). Based on the existence of 1-person game by Ding, Kim and Tan [5], we give a generalization of (GS) in the name of (MQGS) within the framework of Hausdorff topological vector spaces. As an application, we derive an existence result of the generalized vector quasi-variational inequality problem. This result leads to a multi-valued vector quasi-variational inequality extension of the strong vector variational inequality (SVVI) due to Fang and Huang [6] in a general Hausdorff topological vector space.
금상호 한국중국현대문학학회 2003 中國現代文學 Vol.0 No.24
On Chen Chien-Wu's Poems in the Founding Period of Li Poetry Magazine