On the stability of solution mapping for parametric generalized vector quasiequilibrium problems

AbstractIn this paper, we study the solution stability for a class of parametric generalized vector quasiequilibrium problems. By virtue of the parametric gap function, we obtain a sufficient and necessary condition for the Hausdorff lower semicontinuity of the solution mapping to the parametric generalized vector quasiequilibrium problem. The results presented in this paper generalize and improve some main results of Chen et al. (2010) [34], and Zhong and Huang (2011) [35]

Continuity of the Solution Maps for Generalized Parametric Set-Valued Ky Fan Inequality Problems

Under new assumptions, we provide suffcient conditions for the (upper and lower) semicontinuity and continuity of the solution mappings to a class of generalized parametric set-valued Ky Fan inequality problems in linear metric space. These results extend and improve some known results in the literature (e.g., Gong, 2008; Gong and Yoa, 2008; Chen and Gong, 2010; Li and Fang, 2010). Some examples are given to illustrate our results

Including Social Nash Equilibria in Abstract Economies

We consider quasi-variational problems (variational problems having constraint sets depending on their own solutions) which appear in concrete economic models such as social and economic networks, financial derivative models, transportation network congestion and traffic equilibrium. First, using an extension of the classical Minty lemma, we show that new upper stability results can be obtained for parametric quasi-variational and linearized quasi-variational problems, while lower stability, which plays a fundamental role in the investigation of hierarchical problems, cannot be achieved in general, even on very restrictive conditions. Then, regularized problems are considered allowing to introduce approximate solutions for the above problems and to investigate their lower and upper stability properties. We stress that the class of quasi-variational problems include social Nash equilibrium problems in abstract economies, so results about approximate Nash equilibria can be easily deduced.quasi-variational, social Nash equilibria, approximate solution, closed map, lower semicontinuous map, upper stability, lower stability

The existence and the stability of solutions for equilibrium problems with lower and upper bounds

In this paper, we study a class of equilibrium problems with lower and upper bounds. We obtain some existence results of solutions for equilibrium problems with lower and upper bounds by employing some classical fixed-point theorems. We investigate the stability of the solution sets for the problems, and establish sufficient conditions for the upper semicontinuity, lower semicontinuity and continuity of the solution set mapping $S:Lambda_1imesLambda_2o2^{X}$ in a Hausdorff topological vector space, in the case where a set $K$ and a mapping $f$ are perturbed respectively by parameters $lambda$ and $mu.

On operator equilibrium problems

This paper is devoted to study the operator equilibrium problems. By using KKM theorem we give sufficient conditions for the existence of solutions of these problems. As a consequence, existence of solutions for operator variational inequalities and operator minimization problems are derived