与渐近非扩张半群不动点问题相关的分裂等式混合均衡问题及其应用

Split equality equilibrium problems involving fixed point problems for asymptotically nonexpansive semigroups with applications

研究了与渐近非扩张半群不动点问题相关的分裂等式混合均衡问题.在等式约束下,为同时逼近两个空间中混合均衡问题和渐近非扩张半群不动点问题的公共解,借助收缩投影方法引出了一种迭代程序.在适当条件下,该迭代算法的强收敛性被证明.文末还把所得结果应用于分裂等式混合变分不等式问题和分裂等式凸极小化问题.

In this paper, we study the split equation mixed equilibrium problem related to the fixed point problem for asymptotically nonexpansive semigroups. In order to approximate simultaneously a common solution of a mixed equilibrium problem and a fixed point problem for asymptotically nonexpansive semigroup in two spaces under the constraint of split equality, we introduce an iterative process by using the shrinking projection method and prove the strong convergence of the iterative algorithm under suitable conditions. At the end of the paper, we shall apply the results to study the split equality mixed variational inequality problem and the split equality convex minimization problem.