关于m-增生算子方程解的迭代逼近问题的注释

On Remark Iterative Approximation Question of Solutions for m-Accretive Operator Equations

设 E是实一致光滑 Banach空间 ,T:E→ E是 m增生算子 ,且对任意 x,y∈ E,有‖ Tx -Ty‖≤L ( 1 +‖ x -y‖ ) ,其中 L≥ 1 .假设 { un}∞n=0 ,{ vn}∞n=0 为 E中序列 ,{αn}∞n=0 ,{βn}∞n=0 为 [0 ,1 ]中实数列且满足某些条件 ,则 Ishikawa迭代序列 { xn} ∞n=0 强收敛于方程 x +Tx

Let E be a real uniformly smooth Banach space, T:E→E be a m accretive operator,and satisfies condition ‖Tx-Ty‖≤L(1+‖x-y‖ )for any x,y∈E ,and some constant L ≥1.Let {u n} ∞ n=0 ,{v n} ∞ n=0 be two sequences in E ,and {α n} ∞ n=0 , {β n} ∞ n=0 be two real sequences in [0,1] satisfying certain conditions, Then the Ishikawa iteation sequence {x n} ∞ n=0 ,converges strongly to unique solution of the equation x+Tx=f .