一个构造增生映像零点的带误差的迭代算法

An Iterative Algorithm with Errors for Zero Points of Accretive Operators

设E是一致光滑的Banach空间,A:D(A)E→2~E是一个满足值域条件的增生算子,进一步满足线性增长条件:‖Ax‖≤C(1+‖x‖)对某个常数C>0, x∈D(A).设z∈D(A)是任意固定元,x_1∈D(A), A^(-1)0≠Φ.定义序列{x_n}D(A)如下:x_(n+1)∈x_n-λ_n(Ax_n+θ_n(x_n-z+e_n)),n≥1,其中{λ_n}与{θ_n}是满足一定条件的非负数列.则x_n→x~*∈A^(-1)(0),(n→∞).作为应用,我们推出构造连续伪压缩映像的不动点的收敛定理.

Let E be a real uniformly smooth Banach space, A : D(A)■ E→ 2^E be an accretive mapping which satisfies both the range condition and a linear growth condition of the form ‖Ax‖≤C(1 + ‖x‖) for some constant C > 0 and for all x ∈D(A), z ∈D(A) be an arbitrary element and x1 ∈D(A) be an arbitrary initial vector. Suppose A^-10≠Φ.The sequence{xn}■D(A)is defined as follows: xn+1∈xn-λn(Axn +θn(xn-z+en)),for n ≥ 1, where {λn} and {θn} are real non-negative sequences satisfying some conditions.Then xn→x^*∈A^-1(0),(n→∞). As its application, we have deduced a strong convergence theorem for the construction of fixed points for continuous pseudocontractions.