广义平衡问题和一列非扩张映象不动点问题的强收敛定理

Strong convergence theorem for a generalized equilibrium problem and the fixed point problem of an infinite family nonexpansive mappings

在Hilbert空间中,利用Fan-KKM定理,证明了广义平衡问题的辅助问题的解的存在性和唯一性.研究了用于寻找广义平衡问题的的解集和一列非扩张映象的不动点集之公共元的迭代序列,在适当条件下证明了该序列强收敛于这两个集合的公共元.

Using Fan-KKM Theorem, we prove the existence and uniqueness of the solution of the auxiliary problem for a generalized equilibrium problem. A common element of the solution set of the generalized equilibrium problem and the fixed point set for an infinite family of nonexpansive mappings can be achieved by an iterative sequence.