A note on the lower semicontinuity of efficient solutions for parametric vector equilibrium problems

Lower semicontinuity of solutions for order-perturbed parametric vector equilibrium problems

“…The following examples indicate that the assumptionˆin Theorem 3.1 in our work (or the assumption (iii) of Theorem 3.1 in [15]) cannot be applied to the case when AðkÞnSðkÞ ¼ /, for some k 2 K. So the assumptionˆof Theorem 3.1 in our paper (or the assumption (iii) of Theorem 3.1 in [15])is not essential. …”

“…3, we discuss the lower semicontinuity of the (weak) efficient solution mappings for parametric vector equilibrium problems in the case of weakly conditions. Some examples are given to illustrate that the assumptions of the main results in our work or in [15] are only sufficient for some special problems and indicate also that our outcomes are real extension from the corresponding ones in [15].…”

“…Motivated by the idea of variational domination structure, the main results in [15] will be obtained under more weaker conditions in this paper.…”

“…Cheng and Zhu obtained a lower semicontinuity result of the solution mapping to weak vector variational inequalities in finite-dimensional spaces by using the scalarization method (see [14] [15] to the case of set-valued mappings on parametric strong vector equilibrium problems (see [16]). …”

“…Stability may be understood as some types of lower or upper semicontinuity. 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).…”