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We firstly study the inclusion problem of 0∈T(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.