严格伪压缩映像不动点和均衡问题的公共元的迭代算法  

An Iteration Algorithm of Common Elements for Fixed Points About Strict Pseudo-contractive Mappings and Equilibrium Problems

作　　者：刘立红[1] 陈东青[1] 冯光辉[1] 

机构地区：[1]军械工程学院基础部,河北石家庄050003

出　　处：《石家庄铁道大学学报（自然科学版）》2012年第3期103-106,共4页Journal of Shijiazhuang Tiedao University(Natural Science Edition)

基　　金：国家自然科学基金(11071053);军械工程学院基金(YJJXM11003)

摘　　要：均衡问题的解在最优化理论及应用中具有十分重要的意义。物理学和经济学中的很多问题可归结为寻找平衡问题的解。有关非线性算子不动点的迭代构造问题及混合均衡问题的求解方法,许多学者进行了研究。利用杂交投影算法,用以逼近Hilbert空间中严格伪压缩映像不动点集与混合均衡问题解集的公共元,并证明其强收敛性。此算法的最终投影具有显示表达,因而更有利于应用。所得结果改进和推广了最近一些文献的相应结果。The solutions to equilibrium problems is very important in the theory of optimization and applica- tion. Many problems in physics and economics can be ultimately converted to finding a solution to equilibrium problems. Much work has been done in recent years to find iterative schemes to approximate fixed points of non- linear mappings and the solutions about equilibrium problems. A hybrid projection algorithm is proposed to ap- proximate common elements for the set of fixed points of a strict pseudo-contractive mapping and the set of solu- tions to a mixed equilibrium problem in Hilbert spaces, and then its convergence is proved. The iteration algo- rithm is an explicit expression, so it is of great benefit for application. The results obtained in this paper extend and improve some recent results in this area.

关 键 词：严格伪压缩映像 不动点 均衡问题 迭代算法 

分 类 号：O177.91[理学—数学]