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

令E为实一致凸Banach空间,满足Opial条件或其范数是Frechet可微的.令为增生算子,满足值域条件且为非空闭凸子集且满足 .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{Ai}ki=1的公共零点.

Iterative Approximation with Errors of Common Zero Points for a Finite Family of Accretive Operators in Banach Space

Let E be a real uniformly convex Banach space which satisfies Opial's condition or the norm of which is Frechet differentiable. For $i = 1,2,\cdots,k,$ let $A_i: E \rightarrow 2^E$ be accretive operators satisfying the range condition and $\bigcap\limits_{i=1}^{k}A^{-1}_{i}0 \neq \emptyset$. Let $C \subset E$ be a nonempty closed convex set and satisfy that $\overline{D(A_i)}\subset C \subset \bigcap\limits_{r>0}R(I+rA_i),$ for $ i =1,2,\cdots, k.$ A new iterative algorithm with errors is introduced and proved to be weakly convergent to common zero points of accretive operators $\{A_i\}_{i=1}^k$.