局部FC-一致空间内的广义矢量拟变分包含组和广义矢量拟优化问题组

Systems of Generalized Vector Quasi-Variational Inclusions and Systems of Generalized Vector Quasi-Optimization Problems in Locally FC-Uniform Spaces

在没有凸性结构的局部FC-一致空间内,引入和研究了某些新的广义矢量拟变分包含问题组和广义矢量理想(真,帕雷多(Pareto),弱)拟优化问题组.应用KKM型定理和Himmelberg型不动点定理,首先对广义矢量拟变分包含问题组的解,证明了某些新的存在性定理.作为应用,对广义矢量理想(真,帕雷多,弱)拟优化问题组的解也得到了某些新的存在性结果.

Some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal（resp., proper, Pareto, weak）quasi-optimization problems in locally FC-uniform spaces without convexity structure are introduced and studied. By using KKM type theorem and Himmelberg type fixed point theorem, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems were first proved. As applications, some new existence results of solutions for systems of generalized vector quasi-optimization problems were obtained also.