拟变分包含及不动点问题公解的算法

Algorithms of Common Solutions for Quasi Variational Inclusion and Fixed Point Problems

介绍了一种新的迭代算法,在Hilbert空间的框架下,用以寻求具多值极大单调映象和逆-强单调映象的变分包含的解集与非扩张映象的不动点集的公共元.在适当的条件下,逼近于这一公共元的某些强收敛定理被证明.所得结果是新的,它不仅改进和推广了Korpelevich[Ekonomika iMatematicheskie Metody,1976,12(4):747-756]的结果,而且也推广和改进了Iiduka和Takahashi[Non-linear Anal,TMA,2005,61(3):341-350],Takahashi和Toyoda[J OptimTheory Appl,2003,118(2):417-428],Nadezhkina和Takahashi[J Optim Theory Appl,2006,128(1):191-201]及Zeng和Yao[TaiwaneseJournal of Mathematics,2006,10(5):1293-1303]等人的最新结果.

The purpose is to present an iterative scheme for finding a common element of the set of solutions of the variational inclusion problem with multi-valued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space. Under suitable conditions, some strong convergence theorems for approximating to this common elements were proved, The results presented not only improve and extend the main results in Korpelevich [ Ekonomika i Matematichcslde Metody, 1976,12（4） ：747-756] ,but also extend and replenish the corresponding results in Iiduka and Takahashi[ Nonlinear Anal, TMA,2005,61 （3） ：341-3501, Takahashi and Toyoda [J Optim Theory Appl,2003,118（2） ：417-4281, Nadezhldna and Takahashi[ J Optim Theory Appl,2006, 128（ 1 ） ： 191-201 ] and Zeng and Yao[ Taiwan Residents Journal of Mathematics, 2006, 10 （5） ： 1293-1303 .