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| 非扩张映射和广义变分不等式的粘滞逼近法 | |
| 引用本文： | 张丽娟,陈俊敏,侯志彬.非扩张映射和广义变分不等式的粘滞逼近法[J].数学学报,2010,53(4):691-698. |
| 作者姓名： | 张丽娟 陈俊敏 侯志彬 |
| 作者单位： | 1. 河北大学数学与计算机学院 保定 071002; 2. 河北省数学研究中心 石家庄 050016 |
| 基金项目： | 国家自然科学基金资助项目(10971045);河北省自然科学基金数学研究专项项目(07M003)及河北省教育厅资助项目(Z2009111) |
| 摘 要： | 应用已提出的非扩张映射的粘滞逼近方法,给定初值x_0∈C,考虑一般迭代过程{x_n},g(x_(n+1))=α_nf(x_n)+(1-α_n)SP_C(g(x_n)-λ_nAx_n),n≥0,其中{α_n}■(0,1),S:C→C是非扩张映射,C是实Hilbert空间H的非空闭凸子集.在{α_n}满足合适的条件下可证明,{x_n}强收敛到非扩张映射的不动点集和广义变分不等式解的公共元,且满足某变分不等式. |
| 关 键 词： | 粘滞逼近 非扩张映射 变分不等式 |
| 收稿时间： | 2009-02-09 |
| 修稿时间： | 2010-01-20 |
Viscosity Approximation Methods for Nonexpansive Mappings and Generalized Variational Inequalities |
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| Institution: | 1. College of Mathematics and Computer, Hebei University, Baoding 071002, P. R. China; 2. Mathematics Research Center of Hebei Province, Shijiazhuang 050016, P. R. China |
| Abstract: | Viscosity approximation methods for nonexpansive mappings are studied. Consider the general iteration process {xn}, where g(xn+1)=αnf(xn)+(1-αn)SPC(g(xn)-λnAxn), S is a nonexpansive self-mapping of a closed convex subset C of a Hilbert space H. It is shown that {xn} converges strongly to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the Noor variational inequality for an inverse strongly monotone mapping which solves some variational inequality. |
| Keywords: | viscosity approximation nonexpansive mapping variational inequalities |
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