Banach空间中有限个增生算子公共零点的带误差项的迭代逼近

ITERATIVE APPROXIMATION WITH ERRORS OF COMMON ZERO POINTS FOR A FINITE FAMILY OF ACCRETIVE OPERATORS IN BANACH SPACE

令E为实一致凸Banach空间,满足Opial条件或其范数是Frechet可微的.令A_iE×E,i=1,2,…,k为增生算子,满足值域条件且■A_i^(-1)0≠Φ.令CE为非空闭凸子集且满足■R(I+rA_i),i=1,2,…,k.将引入新的带误差项的迭代算法并证明迭代序列弱收敛于{A_i}_(i=1)~k的公共零点.

Let E be a real uniformly convex Banach space which satisfies Opial＇s condition or the norm of which is Frechet differentiable. For i = 1, 2,…, k, let Ai ： E → 2^E be accretive operators satisfying the range condition and κ↑∩↑i=1 Ai^-10≠ Let C ∪→ E be a nonempty closed convex set and satisfy that -↑D（Ai）∪→C∪→∩↑r〉0 R（I＋rAi）, for i = 1, 2, …, k. A new iterative algorithm with errors is introduced and proved to be weakly convergent to common zero points of accretive operators {Au}i=1^k.