On the existence of solutions to systems of vector quasi-optimization problems
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Some sufficient conditions for the existence of solutions to systems of vector quasi-optimization problems are given. These systems also include the systems of quasi-variational inequalities, quasi-equilibrium problems etc. As special case, we obtain some extensions for minimax theorems, general vector optimization problems, general vector quasi-optimization problems, quasi-equilibrium problems... concerning vector functions. From these we generalize some well-known results obtained by Blum and Oettli , Park , Chan and Pang, Parida and Sen , Browder and Minty , Ky Fan , etc.
Key words:Systems of quasi-optimization problems Vector optimizations Quasi-equilibrium problems Ideal points Upper and lower C convex multi-valued mappings Strictly C-quasi-convex and Properly C-quasi-convex multi-valued mappings Upper and lower C-continuous multi-valued mappings
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