On quasivariational inclusion problems of type I and related problems |
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Authors: | Lai-Jiu Lin Nguyen Xuan Tan |
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Affiliation: | (1) Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan;(2) Institute of Mathematics, 18 Hoang Quoc Viet, Hanoi, 10307, Vietnam |
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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.
This work was supported by the National Science Council of the Republic of China and the Academy of Sciences and Technologies
of Vietnam.
The authors wish to express their gratitude to the referees for their valuable suggestions. |
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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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