%0 Journal Article
%T THE EQUIVALENCE BETWEEN THE CONVERGENCES OF MULTI-STEP ITERATIONS WITH ERRORS FOR UNIFORMLY GENERALIZED LIPSCHITZ CONTINUOUS OPERATORS<br>具一致广义Lipschitz连续算子的带误差的多步迭代间的收敛等价性
%A NI Renxing
%A <br>倪仁兴
%J 系统科学与数学
%D 2010
%I 
%X In this paper, the equivalence of the convergence of modified Mann iteration and multi-step Noor iteration with errors is invesgated for uniformly generalized Lipschitz continuous and successively asymptotically $\Phi$-strongly pseudo-contractive type operators in uniformly smooth Banach spaces. In 2007, Zhenyu Huang showed the equivalence of the convergence criteria between modified Mann and Ishikawa iterations with errors for successively $\Phi$-strongly pseudo-contractive operators with bounded range in uniformly smooth Banach spaces. The results obtained in this paper generalize the results of Huang in 2007. The results give an affirmative answer to the conjection raised by Rhoades and Soltuz in 2003.
%K Uniformly generalized Lipschitz continuous operator
%K successively asymptotically $\Phi$-strongly pseudo-contractive type operator<br>一致广义Lipschitz连续算子
%K 逐次渐近$\Phi$-强伪压缩型算子.
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=56F36A4AF46FF2AA8828C0D2BFB10F9A&yid=140ECF96957D60B2&vid=340AC2BF8E7AB4FD&iid=38B194292C032A66&sid=4F0B2F798E08B761&eid=0493D643315CD829&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=12