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Volume 3, Issue 2, 31 August 2021, Pages 149-164
Abstract. In this paper, we introduce and prove the existence of the auxiliary solutions of a weak approximate type to quasi-variational inequalities, (QVI), by using the assumptions of minimal character without recourse to the usual semicontinuity and monotonicity conditions. The concept of weak solutions is linked to a new version of weak approximate normal cones to a closed and convex subset which we support by some examples. Moreover, under a mild additional regularity condition, we establish the convergence of those auxiliary solutions to exact ones wherein a qualitative stability result of approximate fixed points is a key ingredient. Our main result is discussed by an application to Social Nash Equilibria for which we obtain weak approximate solutions under weaker assumptions.
How to Cite this Article:
M. Ait Mansour, J. Lahrache, N. Ziane, Weak approximate solutions to quasi-variational inequalities: Application to social Nash equilibria, Appl. Set-Valued Anal. Optim. 3 (2021), 149-164.