ISHIKAWA ITERATIVE APPROXIMATION OF SOLUTIONS TO EQUATIONS OF LIPSCHITZ STRONGLY ACCRETIVE OPERATORS
Zeng Lu-chuan · Journal of Mathematics · 2004
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.