On the existence of solutions to generalized quasi-equilibrium problems

Authors:
Truong Thi Duong;Nguyen Xuan Tan
Affiliations:
Vinh Technical Teachers Training University, Vinh City, Vietnam;Institute of Mathematics, Hanoi, Vietnam 10307
Venue:
Journal of Global Optimization
Year:
2012

Citing 3
Cited 1

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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.