Abstract
In this paper, we apply new results on variational relation problems obtained by D. T. Luc (J Optim Theory Appl 138:65–76, 2008) to generalized quasi-equilibrium problems. Some sufficient conditions on the existence of its solutions of generalized quasi-equilibrium problems are shown. As special cases, we obtain several results on the existence of solutions of generalized Pareto and weak quasi-equilibrium problems concerning C-pseudomonotone multivalued mappings. We deduce also some results on the existence of solutions to generalized vector Pareto and weakly quasivariational inequality and vector Pareto quasi-optimization problems with multivalued mappings.
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Duong, T.T.T., Tan, N.X. On the existence of solutions to generalized quasi-equilibrium problems. J Glob Optim 52, 711–728 (2012). https://doi.org/10.1007/s10898-011-9700-7
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DOI: https://doi.org/10.1007/s10898-011-9700-7
Keywords
- Generalized quasi-equilibrium problems
- Upper and lower quasivariational inclusions
- Quasi-optimization problems
- Upper and lower \({\mathcal{C}}\)-quasiconvex
- Upper and lower-quasiconvex-like multivalued mappings
- Upper and lower \({\mathcal{C}}\)-continuous multivalued mappings
- C-pseudomonotone
- C-strong pseudomonotone multivalued mappings