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Stability of the set of solutions for generalized vector equilibrium problems with cone constraints

In this paper, the Hausdorff quasi-upper and Hausdorff quasi-lower semicontinuity for set-valued mappings are introduced to derive the upper semicontinuity and lower semicontinuity of cone constraint mapping in normed vector spaces. We discuss existence of solutions for generalized vector equilibrium problems with cone constraints. Moreover, we establish the lower semicontinuity of (weakly) efficient approximate solution mappings, upper semicontinuity of weakly efficient approximate solution mappings, and Hausdorff upper semicontinuity of efficient approximate solution mappings to parametric generalized vector equilibrium problems with cone constraints under some suitable conditions. Some examples are also given to illustrate our main results.