复合Halpern迭代逼近一族m-增生映像公共零点  

Composite Halpern Iteration for Approximating Common Zero of a Finite Family of m-Accretive Mappings

作　　者：田明[1] 程芸[1] 

机构地区：[1]中国民航大学理学院,天津300300

出　　处：《中国民航大学学报》2009年第1期57-59,共3页Journal of Civil Aviation University of China

基　　金：天津市自然科学基金项目(06YFJMJC12500)

摘　　要：在严格凸的Banach空间E中,介绍了一种新的复合迭代方法强收敛到一族m-增生映像公共零点。K是E中非空闭凸子集,假定E的每个非空闭凸子集上的非扩张映像都存在不动点,Ai∶K→E(i=1,2,…,r)是一族m-增生映像,{xn}是由复合Halpern格式定义的迭代序列,证明了当n→∞时,{xn}强收敛于方程Aix=0(i=1,2,…,r)的公共解,改进和推广了Zegeye和Shahzad等人的相应结果。This paper introduces a new composite halpern iteration process for approximating common zero points of m- accretive mappings in Banach spaces. Suppose K is a closed convex subset of a strictly convex real Banach space E which has a uniformly Gateaux differentiable norm. Suppose that every nonempty closed convex bounded subset of E has the fixed point property for nonexpansive mappings. Ai ： K→E（i=1,2, ... ,r）is a family of m-accretive mappings from K to E, {xn} is a sequence defineded by composite Halpern iteration.Then as n→∞, {xn} converges strongly to a common solution of the equations Ai x=0 （i=1,2,..., r）.

关 键 词：Halpem迭代 m-增生映像 零点 

分 类 号：O177.91[理学—数学] O241.7[理学—基础数学]