Algorithms of common solutions to quasi variational inclusion and fixed point problems
Algorithms of common solutions to quasi variational inclusion and fixed point problems
复制标题
DOI：
10.1007/s10483-008-0502-y
复制
发表时间：
2008-06
影响因子：
--
通讯作者：
Shi-sheng Zhang;Joseph H. W. Lee;C. Chan
中科院分区：
文献类型：
--
作者：
Shi-sheng Zhang;Joseph H. W. Lee;C. Chan
本文的目的是提出一种迭代方案，用于寻找具有多值最大单调映射和逆强单调映射的变分包含问题的解集以及希尔伯特空间中非扩张映射的不动点集的共同元素。在适当的条件下，证明了一些近似该共同元素的强收敛定理。论文中提出的结果不仅改进和扩展了Korpelevich (Ekonomika i Matematicheskie Metody, 1976,12(4):747–756)的主要结果，而且扩展和补充了Iiduka和Takahashi (Nonlinear Anal TMA, 2005,61(3):341–350)、Takahashi和Toyoda (J Optim Theory)的相应结果。 Appl, 2003,118(2):417–428)、Nadezhkina 和 Takahashi (J Optim Theory Appl, 2006,128(1):191–201)、Zeng 和 Yao (台湾数学杂志, 2006,10(5):1293–1303)。
The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multivalued 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 this common elements are proved. The results presented in the paper not only improve and extend the main results in Korpelevich (Ekonomika i Matematicheskie Metody, 1976,12(4):747–756), but also extend and replenish the corresponding results obtained by Iiduka and Takahashi (Nonlinear Anal TMA, 2005,61(3):341–350), Takahashi and Toyoda (J Optim Theory Appl, 2003,118(2):417–428), Nadezhkina and Takahashi (J Optim Theory Appl, 2006,128(1):191–201), and Zeng and Yao (Taiwanese Journal of Mathematics, 2006,10(5):1293–1303).