The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption

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• 作者：Zhenyu Huang and Fanwei Bu
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2007
• 出版时间：1 January 2007
• 年：2007
• 卷：325
• 期：1
• 页码：586-594
• 全文大小：130 K

文摘

In this paper we prove some new equivalences between convergence of the Ishikawa and Mann iteration sequences with errors in two schemes by Xu [Y.G. Xu, Ishikawa and Mann iteration process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998) 91–101] and Liu [L.S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995) 114–125], respectively, for strongly successively pseudocontractive mappings. Our main results improve and extend the corresponding results of the all references listed in this article.