锥b-度量空间中向量平衡问题解的存在性

Existence of solutions for vector equilibrium problems in cone b-metric spaces

研究了锥b-度量空间中向量平衡问题解的存在性问题.利用向量空间中的序方法证明了向量形式的Ekeland变分原理,并给出了锥b-度量空间上向量平衡问题解的存在性定理.结果表明,如果向量值函数上半连续且满足向量形式的Ekeland变分原理的条件,那么向量平衡问题的解集非空。

This paper studies the existence of solutions for vector equilibrium problems in cone b-metric spaces.By using the vector ordering method,we prove a vector form of Ekeland＇s variational principle and give the existence theorem of vector equilibrium problems in cone b-metric spaces.Our results show that,if the vector-valued function is upper semi-continuous and satisfies assumptions of the vector form Ekeland＇s variational principle,then the set of solutions for the vector equilibrium problem is nonempty.