自反Banach空间中非扩张非自映射的粘滞迭代逼近方法  

VISCOSITY APPROXIMATION FOR NONEXPANSIVE NONSELF-MAPPINGS IN REFLEXIVE BANACH SPACES

作　　者：宋义生[1] 李庆春[1] 

机构地区：[1]河南师范大学数学与信息科学学院,新乡453007

出　　处：《系统科学与数学》2007年第4期481-487,共7页Journal of Systems Science and Mathematical Sciences

摘　　要：主要在自反和严格凸的且具有一致G■teaux可微范数的Banach空间中研究了非扩张非自映射的粘滞迭代逼近过程,证明了此映射的隐格式与显格式粘滞迭代序列均强收敛到它的某个不动点.Let E be a reflexive Gateaux differentiable norm, and K be and strictly convex Banach space with a uniformly a nonempty closed convex subset of E which is also a sunny nonexpansive retract of E. Assume that T ： K → E is a nonexpansive mapping with F（T） ≠0, and f ： K → K is a fixed contractive mapping. The implicit iterative sequence {xt} is defined by xt = P（tf（xt） ＋ （1 - t）Txt） for t ∈ （0, 1）. The explicit iterative sequence {xn} is given by xn＋1 = P（αnf（xn） ＋ （1 - αn）Txn）, where αn ∈ （0, 1） satisfies appropriate conditions and P is nonexpansive retraction of E onto K. It is shown that {xt} and {xn} strongly converges to a fixed point of T.

关 键 词：非扩张非自映射 粘滞迭代方法 严格凸的 Banach空间. 

分 类 号：O177.2[理学—数学]