On the existence of solutions to systems of vector quasi-optimization problems

Abstract

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 [4], Park [19], Chan and Pang[6], Parida and Sen [18], Browder and Minty [16], Ky Fan [8], etc.