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

doi:10.12341/jssms08950

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (3): 398-409.DOI: 10.12341/jssms08950

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

倪仁兴

绍兴文理学院数学系, 绍兴 312000

收稿日期:2008-12-11 修回日期:1900-01-01 出版日期:2010-03-25 发布日期:2010-03-25

PDF ( 501 ) 引用被引次数 ( 2 | 1 )

倪仁兴. 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[J]. 系统科学与数学, 2010, 30(3): 398-409.

NI Renxing. The Equivalence Between the Convergences of Multi-Step Iterations with Errors for Uniformly Generalized Lipschitz Continuous Operators[J]. Journal of Systems Science and Mathematical Sciences, 2010, 30(3): 398-409.

The Equivalence Between the Convergences of Multi-Step Iterations with Errors for Uniformly Generalized Lipschitz Continuous Operators

NI Renxing

Department of Mathematics, Shaoxing University, Shaoxing 312000

Received:2008-12-11 Revised:1900-01-01 Online:2010-03-25 Published:2010-03-25

研究了一致光滑Banach空间中具一致广义Lipschitz连续的逐次渐近$\Phi$-强伪压缩型算子的具误差的修正Mann迭代和具误差的修正多步Noor迭代间的收敛等价性问题,所得结果是对2007年Zhenyu Huang在一致光滑Banach空间中所建立的逼近具有有界值域的逐次$\Phi$-强伪压缩算子的不动点具误差的修正Mann迭代和具误差的修正Ishikawa 迭代两者的收敛是等价的这一结论更本质的和更一般的推广,所用的方法不全同于Zhenyu Huang所使用的方法,因此,从更一般的意义上肯定地回答了Rhoades和Soltuz于2003年所提出的猜想.

关键词： 一致广义Lipschitz连续算子, 逐次渐近$\Phi$-强伪压缩型算子.

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.

Key words: Uniformly generalized Lipschitz continuous operator, successively asymptotically $\Phi$-strongly pseudo-contractive type operator.

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