向量平衡问题新的存在性定理及其等价形式和应用

New Existence Theorem for Vector Equilibrium Problem and Its Equivalent Version with Applications

对向量值函数引进一个函数关于另一个函数的转移锥半连续性和锥-θ-拟凹性等概念,证明了在函数只需较弱连续性和较弱凸性以及空间不需紧性条件下向量平衡问题解的存在性定理,并给出了它的等价最大元形式.作为应用,证明了若干向量平衡问题和实值平衡问题解的存在性定理,还获得了几个新的集值映射不动点定理.所得结果推广了文献中的相应结果.

For vector-valued functions, the notion of transfer cone semicontinuity of one vector-valued function with respect to another vector-valued function and cone -θ- quasiconcavity are introduced, we prove the existence theorem for vector equilibrium problem relative to the vector-valued functions with weak continuity, weak convexity and without compactness of the space and offer its equivalent maximal version. As applications, we obtain some existence theorems of vector equilibrium problems and real-valued quilibrium problems, while some new fixed point theorems are proved. Our results include some corresponding results in the literatures as special cases.