φ-半压缩算子和φ-强增殖算子方程的迭代  

Iterative Process to φ-Hemicontractive Operator and φ-Strongly Accretive Operator Equations

作　　者：丁协平[1] 张红琳[1] 

机构地区：[1]四川师范大学数学系,成都610066

出　　处：《应用数学和力学》2000年第11期1133-1139,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目!( 198710 59)

摘　　要：设E是任意实Banach空间 ,K是E的非空闭凸子集·　T :K→K是一致连续_半压缩映像且值域有界·　设 an ,bn ,cn ,a′n ,b′n 和 c′n 是 [0 ,1]中的序列且满足条件 :ⅰ )an+bn+cn =a′n+b′n+c′n =1, n≥ 0 ;ⅱ )limbn =limb′n =limc′n =0 ;ⅲ ) ∑∞n =0bn =∞ ;ⅳ )cn =o(bn) ·　对任意给定的x0 ,u0 ,v0 ∈K ,定义Ishikawa迭代 xn 如下 :　　 xn+1=anxn+bnTyn+cnun,yn =a′nxn+b′nTxn +c′nvn　　 ( n≥ 0 ) ,其中un 和 vn 是K中两个有界序列·　则 xn 强收敛于T的唯一不动点·　最后研究了_强增殖算子方程解的Ishikawa迭代收敛性·Let E be an arbitrary real Banach space and K be a nonempty closed convex subsets of E. Let T:K→K be a uniformly continuous _ hemicontractive operator with bounded range and a n,b n,c n,a ′ n,b ′ n,c ′ n be sequences in [0,1] satisfying:ⅰ) a n+b n+c n=a ′ n+b ′ n+c ′ n=1A ·D2n≥0;ⅱ) lim b n= lim b ′ n= lim c ′ n=0;ⅲ)∑∞n=0b n=∞;ⅳ) c n=o(b n)A ·D2 For any given x 0,u 0,v 0∈K,define the Ishikawa type iterative sequence x n as follows: x n+1 =a nx n+b nTy n+c nu n, y n=a ′ nx n+b ′ nTx n+c ′ nv n (n≥0), where u n and v n are bounded sequences in K. Then x n converges strongly to the unique fixed point of T. Related result deals with the convergence of Ishikawa type iterative sequence to the solution of _strongly accretive operator equations.

关 键 词：￠-强增殖算子 ￠-半压缩算子 ISHIKAWA迭代序列 BANACH空间 算子方程 

分 类 号：O177.2[理学—数学] O177.91[理学—基础数学]