逐次渐近Φ-强半压缩型有限算子簇的多步迭代程序的收敛性  

The Convergences of Mulit-Step Iterations for a Finite Family of Successively Asymptotically StronglyΦ-Hemicontractive Type Operations

作　　者：倪仁兴[1] 余丽云[2,1] 

机构地区：[1]绍兴文理学院数学系,绍兴312000 [2]浙江师范大学数理信息工程学院,金华321004

出　　处：《数学学报（中文版）》2010年第3期477-488,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10971194);浙江省自然科学基金资助项目(Y606717)

摘　　要：对一致广义Lipschitz连续的逐次渐近Φ-强半压缩型有限算子簇,研究了一致光滑Banach空间中具误差的修正多步Noor迭代序列强收敛于该算子簇的公共不动点问题.作为所得结果的应用,得到了2007年Huang在相同空间框架中所建立的逼近具有有界值域的逐次Φ-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果,而且所用的方法不同于Huang.同时还改进和推广了Rhoades和Soltuz,Huang,Bu和Noor,Huang和Bu,Su,Yao,Chen和Zhou,Liu,Kim,Kim,Liu,Ni和Xu等人的近期相应结果.In this paper,the problems which modified multi-step Noor iterations with errors converges strongly to a common fixed point are invesgated for a finite family of uniformly generalized Lipschitz continuous and successively asymptotically stronglyΦ-hemicontractive type operators in uniformly smooth Banach spaces.As application, it is obtained that the result of Huang Zhenyu at 2007 concerning the equivalence of the convergence criteria between modified Mann iterations with errors and modified multi-step Noor iterations with errors for successivelyΦ-strongly pseudo-contractive operators with bounded range in same spaces.Furthermore,the methods of proofs are quite different from Huang Zhenyu＇s.Meanwhile,these results improve and generalize many recent corresponding results obtained by Rhoades,Soltuz,Huang,Bu,Noor, Huang,Bu,Su,Yao,Chen,Zhou,Liu,Kim,Kim,Liu,Ni,Xu and the other authors.

关 键 词：逐次渐近Φ-强半伪压缩型有限算子簇 一致广义Lipschitz连续算子 具误差的修正Mann迭代 

分 类 号：O177.91[理学—数学]