增生型算子方程解的具有混合误差项的迭代程序

Iterative process with mixed errors of solutions for accretive type operator equations

设E是任意实Banach空间,T:E→E是Lipschitz增生算子,在没有条件limn→∞αn=limn→∞βn=0之下,证明了非线性算子方程x+Tx=f解的具有混合误差项的Ishikawa迭代程序的收敛性问题,并提供了收敛率的估计.结果改进和推广了近期的一些相关结果.

Let E be an arbitrary real Banach space, and T：E→E be a Lipschitz accretive operator. Under the lack of the condition limn→∞αn = lim n→∞βn =0, the convergence of Ishikawa iterative process with mixed errors for solutions of the nonlinear equation x ＋ Tx =f is proved, and a convergence rate estimate is provided. These results improve and extend some recent corresponding results.