On Vector Quasivariational Inequalities

Lee, Gue Myung; Lee, Byung-Soo; Chang, Shih-sen

doi:10.1006/jmaa.1996.0401

Cited by 50 publications

(18 citation statements)

References 12 publications

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“…Chen and Cheng [5] proposed the vector variational inequality in an infinite-dimensional space and applied it to the vector optimization problem. Since then, many authors have extensively studied various types of vector variational inequalities in abstract space (see, for example, [4,6,8,9,11,14,21,27,28,30,33,37,38] and the references therein). Recently, some authors have investigated the optimality conditions for vector variational inequalities.…”

Section: Introductionmentioning

confidence: 99%

Optimality conditions for the Henig efficient solution of vector equilibrium problems with constraints

2010

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The purpose of this paper is to establish optimality conditions for vector equilibrium problems with constraints. By using the separation of convex sets, we obtain the necessary and sufficient conditions for the Henig efficient solution and the superefficient solution to the vector equilibrium problem with constraints. As applications of our results, we derive some optimality conditions to the vector variational inequality problem and the vector optimization problem with constraints.

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Section: Introductionmentioning

confidence: 99%

Optimality conditions for the Henig efficient solution of vector equilibrium problems with constraints

2010

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“…(II) In 1996, Lee et al [40] also applied the 1992 theorem to a vector version of the main result of [36], which is an existence theorem for the vector quasi-variational inequality for multimaps with vector values.…”

Section: Comments On Some Related Resultsmentioning

confidence: 99%

Applications of some basic theorems in the KKM theory

Park

2011

Fixed Point Theory Appl

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In this review, we introduce a new KKM-type theorem for intersectionally closedvalued KKM map on abstract convex spaces and its direct consequences such as a Fan-Browder-type fixed point theorem and maximal element theorems. For these basic theorems of the KKM theory, we review previously obtained particular consequences of them mainly due to the author and their recent applications obtained by other authors. Therefore, those applications might be improved by following our new results. 2010 Mathematics Subject Classification: 47H04; 47H10; 52A99; 54H25; 55M20; 58E35; 90D13.

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“…This problem was also called generalized vector quasi-variational-like inequality and studied with certain monotonicity by Ding [13], and problem (1.4) contains as special cases the generalized vector variational-like inequality in [1,2,14,15,28] and the generalized vector quasi-variational inequality studied by Chen and Li [10] and Lee et al [22] and those vector variational inequalities in [6-9, 11, 12, 16, 19-21, 23, 26, 30, 33-37].…”

Section: ∀Y ∈ D(x) T(x)η(yx) + H(x Y) ⊆ −Int C(x)mentioning

confidence: 99%