Approximating solution of 0T(x) for an H-accretive operator in Banach spaces

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• 作者：Sanyang Liu^a ; ^{liusanyang@126.com"" rel=""nofollow} ; Huimin He ; ^a ; ^{huiminhe@126.com"" rel=""nofollow}
• 关键词：H-accretive operators ; Resolvent operator ; Iteration algorithms ; Strong convergence ; Weak convergence
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 出版时间：1 January 2012
• 年：2012
• 卷：385
• 期：1
• 页码：466-476
• 全文大小：211 K

文摘

We firstly study the inclusion problem of 0T(x) for an H-accretive operator introduced in [Yaping Fang, Nanjing Huang, H-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces, Appl. Math. Lett. 17 (2004) 647–653] in Banach spaces and obtain strong convergence theorems and weak convergence theorems. Simultaneously, we analyze the relations between m-accretive operators and H-accretive operators and give some numerical examples to explain main results. The main results presented in this paper mainly extend and improve the results of [Tomas Dominguez Benavides, Genaro Lopez Acedo, Hong-Kun Xu, Iterative solutions for zeros of accretive operators, Math. Nachr. 248–249 (2003) 62–71] and [Hong-Kun Xu, Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006) 631–643] from m-accretive operators to H-accretive operators.