Lipschitz严格伪压缩映象的具误差的迭代逼近

Iterative Approximation with Errors for Lipschitz Strictly Pseudocontractive Mappings

设 K 是任意实 Banach 空间 E 的非空闭凸子集,T : K → K 是 Lipschitz 严格伪压缩映 象。本文给出一个新的具误差的 Ishikawa 迭代程序强收敛到 T 的唯一不动点,并给出一个涉 及 Lipschitz 强增生映象 T 的非线性方程 Tx = f 的解的迭代逼近。本文结果通过去掉空间 E 的 ∞ 一致光滑或 p? 一致光滑的严格要求、K 的有界性、 lim αn = lim βn = 0 和 αn < ∞(s > s n→∞ n→∞ n=0 1) 的限制而得到。

Suppose that K is a nonempty closed convex subset of an arbitrary real Banach space E. Let T : K → K be a Lipschitz strictly pseudocontractive mapping. In this paper, a new Ishikawa iterative sequence with errors which converges strongly to the unique ?xed point of T is given. The author presents a related result that the new Ishikawa iterative with errors converges to a solution of the nonlinear equation Tx = f when T is Lipschitz strongly accretive mapping. The results are obtained by removing the strict conditions of space E being uniformly smooth or P? uniformly smooth, the ∞ boundedness of K, lim αn = lim βn = 0 and αn < ∞(s >). s n→∞ n→∞ n=0