Abstract
The purpose of this article is to establish some results on the existence and generic stability of solution sets of the controlled system for multiobjective generalized games in infinite-dimensional spaces. First, we introduce a class of the controlled system for multiobjective generalized games. Afterward, we establish some conditions for existence of the solution set to this problem using the Kakutani–Fan–Glicksberg fixed-point theorem. Finally, we study the generic stability of set-valued mappings where the set of essential points of a map is a dense residual subset of a (Hausdorff) metric space of the set-valued maps. The results presented in the paper are new and completely different from the main results given by some authors in the literature.
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Acknowledgements
This research was supported by Ministry of Education and Training of Vietnam under grant number B2021.SPD.03. The authors are grateful to the editor and two anonymous referees for their valuable remarks which improved the results and presentation of this article.
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Hung, N.V., Keller, A.A. Existence and generic stability conditions of equilibrium points to controlled systems for n-player multiobjective generalized games using the Kakutani–Fan–Glicksberg fixed-point theorem. Optim Lett 16, 1477–1493 (2022). https://doi.org/10.1007/s11590-021-01786-1
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DOI: https://doi.org/10.1007/s11590-021-01786-1
Keywords
- Kakutani–Fan–Glicksberg fixed-point theorem
- Control system for multiobjective generalized game
- Existence conditions
- Generic stability