Semicontinuity of Approximate Solution Mappings to Parametric Set-Valued Weak Vector Equilibrium Problems

Strong vector equilibrium problems with LSC approximate solution mappings

“…(ii) The results of [14,18] are valid under some generalized cone-concavity condition for F (t, •, η) which is different from condition (iii) of Corollary 12.…”

“…The stability for exact solutions is among the most important research topics in the theory of parametric equilibrium problems and is discussed in many papers (see e.g. [2,4,5,8,11,13,15,17,18,20,21,22] and the references therein). However, it is known (see e.g.…”

“…Anh and Khanh [1] have investigated the lower/upper semicontinuity and the Hausdorff lower/upper semicontinuity of two kinds of approximate solution mappings of parametric generalized vector quasiequilibrium problems. Li and Li [14] and Peng et al [18] have treated the continuity of the approximate solution mapping of a parametric weak vector equilibrium problem with cone-convex set-valued maps by linear scalarization approaches. It is worth noting that all the papers [1,14,18] deal with weak versions of parametric vector equilibrium problems.…”

“…Li and Li [14] and Peng et al [18] have treated the continuity of the approximate solution mapping of a parametric weak vector equilibrium problem with cone-convex set-valued maps by linear scalarization approaches. It is worth noting that all the papers [1,14,18] deal with weak versions of parametric vector equilibrium problems. In this paper, we are interested in the stability of the approximate solution mapping for a strong case of parametric vector equilibrium problems which is formulated as follows.…”

“…To our knowledge, stability results for the approximate solution mapping of Problem (P 1 t ) are not found in the literature. The case of Problem (P 2 t ) is investigated in [14,18], under the assumptions different from ours in several ways:…”