Banach空间中集值平衡问题解的迭代算法

Iterative Schemes for Solving Multivalued Equilibrium Problem in Banach Spaces

在自反Banach空间中研究了集值平衡问题解的存在性和迭代算法.首先,给出了伪单调集值映射的定义,并将该定义与已有的伪单调单值映射的定义进行了比较.其次,应用KKM定理证明了集值平衡问题解的存在性.然后,利用辅助原理,构造了集值平衡问题解的迭代算法,还应用KKM定理证明了辅助变分不等式解的存在性.最后,在集值映射是伪单调的假设条件下证明了迭代序列的收敛性.推广和统一了最近一些文献上的相关结果.

In this paper,we introduce the concept of pseudomonotonicity of a multivalued mapping and develop some iterative schemes for finding the approximate solutions of multivalued equilibrium problem in reflexive Banach spaces.We use the concept of pseudomonotonicity to prove the convergence of the approximate solutions to the exact solution of multivalued equilibrium problem.It is worth notice that we do not assume Lipschitz continuity of any mappings in this paper.