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On the existence of solutions to generalized quasi-equilibrium problems

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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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Correspondence to Nguyen Xuan Tan.

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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).

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