Stability for parametric implicit vector equilibrium problems

Huang, Nan; Li, Jun; Thompson, H. B.

doi:10.1016/j.mcm.2005.06.010

Cited by 96 publications

(31 citation statements)

References 17 publications

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“…At the same time, vector variational inequalities and vector complementarity problems have found many of its applications in vector optimization, set-valued optimization, approximate analysis of vector optimization problems and vector network equilibrium problems. For details, we refer to [4,12,14] and the references therein.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

General Mixed Vector F-Implicit Complementarity Problems in Banach Spaces

Wu¹,

Huang²

2008

Journal of Applied Analysis

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Abstract. In this paper, we introduce a new class of general mixed vector F -implicit complementarity problems and general mixed vector F -implicit variational inequality problems, and study the equivalence between of them under certain assumptions in Banach spaces. We also derive some new existence theorems of solutions for the general mixed vector F -implicit complementarity problems and the general mixed vector F -implicit variational inequality problems by using the FKKM theorem under some suitable assumptions without monotonicity. Moreover, we establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution mapping of the general mixed vector Fimplicit variational inequality problems.2000 Mathematics Subject Classification. Primary: 90C33, 49J40.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

General Mixed Vector F-Implicit Complementarity Problems in Banach Spaces

Wu¹,

Huang²

2008

Journal of Applied Analysis

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“…The stability and sensitivity analyses may be understood in two ways. The first is the semicontinuity, continuity (or Hausdorff continuity) of solution mappings [3,5,7,10,20,26,30,31] and references therein. The second is the Hölder/Lipschitz continuity of solution mappings [1,2,4,6,8,9,13,17,18,21,[32][33][34].…”

Section: Introductionmentioning

confidence: 99%

On Hölder continuity of approximate solution maps to vector equilibrium problems

Anh¹,

Nguyen²,

Tam³

2017

Turk J Math

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In this article, we consider parametric vector equilibrium problems in normed spaces. Sufficient conditions for Hölder continuity of approximate solution mappings where they are set-valued are established. As applications of these results, the Hölder continuity of the approximate solution mappings for vector optimization problems and vector variational inequalities are derived at the end of the paper. Our results are new and include the existing ones in the literature.

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“…The concept of well-posedness is motivated by the numerical methods producing approximating sequences. So, many authors were devoted to generalizing the concept of wellposedness of optimization problems (see [1,3]), variational inequalities (see [4][5][6]19]), fixed point problems (see [17]), equilibrium problems (see [14,15,[20][21][22]) and inclusion problems (see [2]) etc.…”

Section: Introductionmentioning

confidence: 99%

On the well-posedness of the generalized split quasi-inverse variational inequalities

Cao¹,

Kong²,

Zeng³

2016

J. Nonlinear Sci. Appl.

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In this paper, a generalized split quasi-inverse variational inequality ((GSQIVI), for short) is considered and investigated in Hilbert spaces. Since the well-posedness results, not only show us the qualitative properties of problem (GSQIVI), but also it gives us an outlook to the convergence analysis of the solutions for (GSQIVI). Therefore, we first introduce the concepts concerning with the approximating sequences, well-posedness and well-posedness in the generalized sense of (GSQIVI). Then, under those definitions, we establish several metric characterizations and equivalent conditions of well-posedness for the (GSQIVI) by using the measure of noncompactness theory and the generalized Cantor theorem. c 2016 All rights reserved.Keywords: Generalized split quasi-inverse variational inequality, measure of noncompactness, well-posedness, Painlevé-Kuratowski limits. 2010 MSC: 49J53, 49K40, 90C33, 90C46.

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Stability for parametric implicit vector equilibrium problems

Cited by 96 publications

References 17 publications

General Mixed Vector F-Implicit Complementarity Problems in Banach Spaces

General Mixed Vector F-Implicit Complementarity Problems in Banach Spaces

On Hölder continuity of approximate solution maps to vector equilibrium problems

On the well-posedness of the generalized split quasi-inverse variational inequalities

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