Author(s)

Xianzheng Dong, Chi Zhang, Lizhi Zhang

Jiangxi V & T College of Communications, Nanchang, China.

The stability analysis of the solution mappings for vector equilibrium problems is an important topic in optimization theory and its applications. In this paper, we focus on the continuity of the solution mapping for a parametric generalized strong vector equilibrium problem. By virtue of a nonlinear scalarization technique, a new density result of the solution mapping is obtained. Based on the density result, we give sufficient conditions for the lower semicontinuity and the Hausdorff upper semicontinuity of the solution mapping to the parametric generalized strong vector equilibrium problem. In addition, some examples were given to illustrate that our results improve ones in the literature.

Parametric Generalized Strong Vector Equilibrium Problem, Lower Semicontinuity, Hausdorff Upper Semicontinuity, Nonlinear Scalarization

Dong, X. , Zhang, C. and Zhang, L. (2021) Continuity of the Solution Mappings for Parametric Generalized Strong Vector Equilibrium Problems. Advances in Pure Mathematics, 11, 937-949. doi: 10.4236/apm.2021.1112060.