Banach空间中含强增生算子的非线性方程的迭代解  

Iterative Solution of Nonlinear Equations with Strongly Accretive Operators in Banach Spaces

作　　者：周海云[1] 

机构地区：[1]军械工程学院基础部

出　　处：《应用数学和力学》1999年第3期269-276,共8页Applied Mathematics and Mechanics

摘　　要：设Ｘ为实Ｂａｎａｃｈ空间，Ｘ为其一致凸的共轭空间·设Ｔ：Ｘ→Ｘ为Ｌｉｐｓｃｈｉｔｚｉａｎ强增生映象，Ｌ≥１为其Ｌｉｐｓｃｈｉｔｚｉａｎ常数，ｋ∈（０，１）为其强增生常数·设αｎ｛｝，βｎ｛｝为［０，１］中的两个实数列满足：（ⅰ）αｎ→０（ｎ→∞）；（ⅱ）βｎ＜ｋ（１－ｋ）Ｌ（１＋Ｌ）（ｎ≥０）；（ⅲ）∑∞ｎ＝０αｎ＝∞·假设ｕｎ｛｝∞ｎ＝０和ｖｎ｛｝∞ｎ＝０为Ｘ中两序列满足：‖ｕｎ‖＝ｏ（αｎ）与ｖｎ→０（ｎ→∞）·任取ｘ０∈Ｘ，则由（ＩＳ）１ｘｎ＋１＝（１－αｎ）ｘｎ＋αｎＳｙｎ＋ｕｎｙｎ＝（１－βｎ）ｘｎ＋βｎＳｘｎ＋ｖｎ（ｎ≥０）｛所定义的迭代序列ｘｎ｛｝强收敛于方程Ｔｘ＝ｆ的唯一解·一个相关结果处理φ＿半压缩映象的不动点的迭代逼近·Let X be a real Banach space with a uniformly convex dual X * . Let T:X→X be a Lipschitzian and strongly accretive mapping with a Lipschitzian constant L≥1 and a strongly accretive constant k∈(0,1) . Let α n,β n be two real sequences in satisfying: (ⅰ) α n→0 as n→∞; (ⅱ) β n<k(1-k)L(1+L), for all n≥0; (ⅲ) ∑∞n=0α n=∞ . Set Sx=f-Tx+x,x∈X . Assume that u n ∞ n=0 and v n ∞ n=0 be two sequences in X satisfying ‖u n‖=o(α n) and v n→0 as n→∞ . For arbitrary x 0∈X, the iteration sequence x n is defined by ( IS) 1x n+1 =(1-α n)x n+α nSy n+u n y n=(1-β n)x n+β nSx n+v n (n≥0) then x n converges strongly to the unique solution of the equation Tx=f . A related result deals with iterative approximation of fixed points of φ_ hemicontractive mappings.

关 键 词：巴拿赫空间 强增生算子 迭代解 非线性方程 

分 类 号：O177.91[理学—数学]