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Generic stability of the solution set for symmetric vector quasi-equilibrium problems under the condition of cone-convexity. (Chinese. English summary) Zbl 1240.49009

Summary: In topological vector spaces, a new existence result on the weakly Pareto solutions for vector quasi-equilibrium problem is obtained by the Ky Fan’s section theorem. As an application, a new existence theorem of the weakly Pareto solutions for symmetric vector quasi-equilibrium problem is obtained under the condition that its payoff functions are cone-convex. The theorem, under weaker conditions, solves the second problem proposed by J. Y. Fu [J. Math. Anal. 285, No. 2, 708–713 (2003; Zbl 1031.49013)], whether there is a weakly Pareto solution for symmetric vector quasi-equilibrium problem when its payoff functions are cone-convex. Finally, the authors discuss the generic stability of the solution set for symmetric vector quasi-equilibrium problem under the condition of cone-convexity in normed linear spaces.

MSC:

49J40 Variational inequalities
49K40 Sensitivity, stability, well-posedness
47J20 Variational and other types of inequalities involving nonlinear operators (general)

Citations:

Zbl 1031.49013
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