Existence of Solutions to General Quasiequilibrium Problems and Applications

Hải, Nguyễn Xuân; Khánh, Phan Quốc

doi:10.1007/s10957-007-9170-8

Cited by 56 publications

(12 citation statements)

References 19 publications

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“…Many efforts have been made for the last decade to propose general setting problems related to optimization, beginning with [5] where an equilibrium problem has been considered, see, e.g., [2][3][4]6,10,12,16].…”

Section: Introductionmentioning

confidence: 99%

The solution existence of general variational inclusion problems

Hải

Khánh

2007

Journal of Mathematical Analysis and Applications

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We propose general variational inclusion problems which are slightly different from corresponding problems considered in several recent papers in the literature and show that they are advantageous. Sufficient conditions for the solution existence are established. As applications we derive consequences for several special cases of variational inclusion problems, quasioptimization problems, equilibrium problems and implicit variational inequalities and show that they improve the results of some recent existing papers.

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Section: Introductionmentioning

confidence: 99%

The solution existence of general variational inclusion problems

Hải

Khánh

2007

Journal of Mathematical Analysis and Applications

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“…To end this subsection, notice that by similar arguments we can consider quasiequilibrium problems with other types of constraints, e.g., with those studied in [16] and [17]. Of course, then stability results are derived as consequences of properties of quasivariational inclusion problems with the corresponding constraints.…”

Section: If E Is Inner Open Star-inner Semicontinuous or Lsc Atλ Thmentioning

confidence: 99%

About Semicontinuity of Set-valued Maps and Stability of Quasivariational Inclusions

Anh

Khánh

Quy

2014

Set-Valued Var. Anal

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We propose several additional kinds of semi-limits and corresponding notions of semicontinuity of a set-valued map. They can be used additionally to known basic concepts of semicontinuity to have a clearer insight of local behaviors of maps. Then, we investigate semicontinuity properties of solution maps to a general parametric quasivariational inclusion, which is shown to include most of optimization-related problems. Consequences are derived for several particular problems. Our results are new or generalize/improve recent existing ones in the literature.

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“…These problems, or more general equilibrium problems, are studied in many papers (see, for instance, [5,7,8,[12][13][14][15][16][17])…”

Section: Applicationsmentioning

confidence: 99%