Lipschitz强增生算子方程解的Ishikawa迭代逼近

ISHIKAWA ITERATIVE APPROXIMATION OF SOLUTIONS TO EQUATIONS OF LIPSCHITZ STRONGLY ACCRETIVE OPERATORS

设E是任意实Banach空间 ,T∶E→E是Lipschitz强增生算子 .在无需假设limn→∞αn=limn→∞βn=0之下 ,本文证明了带误差的Ishikawa迭代序列强收敛到方程Tx =f的唯一解 .而且还提供了该序列的某些特例的收敛率估计 .另外 ,相关结果也讨论了E中Lipschitz强伪压缩映象的不动点的Ishikawa迭代逼近问题 .

Let E be an arbitrary real Banach space, and T∶E→E be a Lipschitz strongly accretive operator. Under the lack of the condition (lim)n→∞α_n=(lim)n→∞β_n=0, it is shown that the Ishikawa iterative sequence with errors converges strongly to the unique solution of the equation Tx=f. Moreover, the convergence rate estimate of some special cases of such a sequence is established. On the other hand, a related result also discusses the Ishikawa iterative approximation problem of fixed points of Lipschitz strongly pseudocontractive mappings in E. The results in this paper improve and extend some recent results in the present literature.