Banach空间中非扩张映射不动点的粘性逼近方法  

VISCOSITY APPROXIMATION METHODS FOR FIXED POINT OF NONEXPANSIVE MAPPINGS IN BANACH SPACES

作　　者：唐艳[1] 

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《数学杂志》2013年第1期99-104,共6页Journal of Mathematics

基　　金：国家自然科学基金项目(11001287);重庆市教委科技研究项目(KJ 110701)

摘　　要：本文研究了非扩张映射不动点的逼近问题的迭代方法.利用粘性逼近方法,在具有一致Gateaux可微范数的Banach空间中,获得了迭代序列的强收敛性,并说明了该序列强收敛于某变分不等式的唯一解.该方法推广了某些文献的结果.In this article, we study the iterative method for approximating the fixed point of nonexpansive mappings. Based on the viscosity iterative scheme, strong convergence of the iterative sequence is obtained in a real Banach space with a uniformly Gateaux differentiable norm. Under some suitable conditions, we prove that the iterative sequence convergence strongly to the unique solution of a variational inequality, which extends the result of some literature.

关 键 词：非扩张映射 不动点 粘性逼近方法 强收敛 变分不等式 

分 类 号：O177.91[理学—数学]