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

作　　者：李杨 Li Yang(School of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing 210023,China)

机构地区：[1]南京财经大学应用数学学院,江苏南京210023

出　　处：《纯粹数学与应用数学》2020年第1期80-93,共14页Pure and Applied Mathematics

基　　金：江苏省自然科学基金(BK20171041);江苏省高校自然科学研究面上项目(16KJB110009);江苏高校哲学社会科学研究项目(2017SJB0238).

摘　　要：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.

关 键 词：分裂等式混合均衡 渐近非扩张半群 不动点 强收敛 

分 类 号：O177.91[理学—数学]