Hilbert空间中广义平衡问题和不动点问题的粘滞逼近法  

Viscosity Approximation Methods for Generalized Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

作　　者：刘英[1] 苏珂[1] 

机构地区：[1]河北大学数学与计算机学院,保定071002

出　　处：《数学学报（中文版）》2010年第2期363-374,共12页Acta Mathematica Sinica：Chinese Series

基　　金：河北省教育厅资助项目(Z2009111)

摘　　要：在Hilbert空间,我们用粘滞逼近法建立了一迭代序列来逼近两个集合的公共点,这两个集合分别是广义平衡问题的解集和渐进非扩张映射的不动点集.我们表明这一迭代序列强收敛到这两个集合的公共点,而且这一公共点还是一变分不等式的解.用这一结果,还研究了三个强收敛问题和优化问题.We introduce an iterative sequence by the viscosity approximation method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of an asymptotically nonexpansive mapping in a Hilbert space and then obtain that the sequence converges strongly to a common element of two sets which solves some variational inequality. Using this result, we study three strong convergence problems and the optimization problem.

关 键 词：粘滞逼近法 平衡问题 渐进非扩张映射 

分 类 号：O177.91[理学—数学]