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Vietnam Journal of Mathematics 34:4(2006) 423-440  On Systems of Quasivariational Inclusion Problems of Type I and Related Problems Lai-Jiu Lin and Nguyen Xuan Tan Abstract.  The systems of quasivariational inclusion problems are introduced and sufficient conditions on the existence of their solutions are shown. As special cases, we obtain several results on the existence of solutions of quasivariational inclusion problems, general vector ideal (proper, Pareto, weak) quasi-optimization problems, quasivariational inequalities, and vector quasi-equilibrium problems etc.   2000 Mathematics Subject Classification: 90C, 90D, 49J. Keywords: Upper quasivariational inclusions, lower quasivariational inclusions, $\alpha$ quasi-optimization problems, vector optimization problem, quasi-equilibrium problems, upper and lower $C$-quasiconvex multivalued mappings, upper and lower $C$- continuous multivalued mappings.

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