Abstract
The lower semicontinuity of the (weak) efficient solution mappings for parametric vector equilibrium problems under more weaker assumptions is established. Some examples are developed to illustrate our results are real generalization different from recent ones in the literature and to describe the essential conditions of the latest results in the references are not real essential.
Highlights
Several classes of problems, including the vector variational inequality problem, the vector complementarity problem, the vector optimization problem and the vector saddle point problem, have been unified as a model of the vector equilibrium problem, which has been intensively studied in the literature
The semicontinuity, especially the lower semicontinuity, of the solution mappings for parametric vector equilibrium problems has been intensively studied in various directions
Anh and Khanh first obtained the semicontinuity of the solution mappings of parametric multivalued vector quasiequilibrium problems, and obtained verifiable sufficient conditions for solution sets of general quasivariational inclusion problems to have these semicontinuity-related properties and discussed in detail a traffic network problem as a sample for employing the main results in practical situations, and latter established sufficient conditions for lower and Hausdorff lower semicontinuity, upper semicontinuity, and continuity of solution mappings of parametric quasi-equilibrium problems in topological vector spaces
Summary
Lower semicontinuity of solutions for order-perturbed parametric vector equilibrium problems. This article is published with open access at Springerlink.com
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