Journal of Global Optimization

, Volume 39, Issue 3, pp 393–407

# On quasivariational inclusion problems of type I and related problems

• Lai-Jiu Lin
• Nguyen Xuan Tan
Original Paper

## Abstract

The quasivariational inclusion problems are formulated and sufficient conditions on the existence of solutions are shown. As special cases, we obtain several results on the existence of solutions of a general vector ideal (proper, Pareto, weak) quasi-optimization problems, of quasivariational inequalities, and of vector quasi-equilibrium problems. Further, we prove theorems on the existence for solutions of the sum of these inclusions. As corollaries, we shall show several results on the existence of solutions to another problems in the vector optimization problems concerning multivalued mappings.

## Keywords

Upper quasivariational inclusions Lower quasivariational inclusions α 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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