Among many approaches for dealing with the lower semicontinuity and continuity of solution mappings for parametric vector variational inequalities and parametric vector equilibrium problems, the scalarization method is of considerable interest.
The lower semicontinuity of the (weak) efficient solution mappings for parametric vector equilibrium problems under more weaker assumptions is established.
Zhang et al. obtained the lower semicontinuity of solution mappings for parametric vector equilibrium problems under the Höder-related assumptions [15].
3, we discuss the lower semicontinuity of the (weak) efficient solution mappings for parametric vector equilibrium problems in the case of weakly conditions.
Recently, the semicontinuity, especially the lower semicontinuity, of the solution mappings for parametric vector equilibrium problems has been intensively studied in various directions (see [1, 2, 4, 6, 10, 15] and references therein).
Huang et al. used local existence results to establish the lower semicontinuity of solution mappings for parametric implicit vector equilibrium problems (see [7]).
Most recently, Bednarczuk [12] defined weak sharp minima of order for vector-valued mappings under an assumption that the order cone is closed, convex, and pointed and used the concept to prove upper Hölderness and Hölder calmness of the solution set-valued mappings for a parametric vector optimization problem.
Huang et al. [6] used local existence results of the models considered and additional assumptions to establish the lower semicontinuity of solution mappings for parametric implicit vector equilibrium problems.
Recently, in a linear setting, many authors focused on the existence of solutions to equilibrium problems for vector mappings; see, for example, Ansari and Yao [6], Ansari and Flores-Bazán [7], Fu [8], Fu and Wan [9], Khan [10], Khan et al. [11], Khan and Chen [12], Hou et al. [13], Iusem and Sosa [14], Chen et al. [15], Kassay et al. [16], and the authors referenced by their works.
