关于非扩张映象的最近的公共不动点问题

张石生

关于非扩张映象的最近的公共不动点问题

张石生^1,2

1.
宜宾学院数学系,四川宜宾 644007;2.四川大学数学系,成都 610064

详细信息

作者简介:
张石生(1934- ),男,云南曲靖人,教授(E-mail:sszhang_1@yahoo.com.cn).

中图分类号: O177.91
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- 被引次数: 0
出版历程
- 收稿日期: 2004-12-03
- 修回日期: 2006-04-11
- 刊出日期: 2006-07-15

On the Problem of Nearest Common Fixed Point of Nonexpansive Mappings

ZHANG Shi-sheng^1,2

1.
Department of Mathematics, Yibin University, Yibin, Sichuan 644007, P. R. China;

摘要

摘要: 利用粘性逼近方法，在自反Banach空间的框架下,研究无限族非扩张映象及对给定的压缩映象的迭代程序的收敛性问题．在适当的条件下，证明了该迭代序列强收敛于某一公共不动点,而且这一公共不动点也是自反Banach空间中某一变分不等式的唯一解．所得结果改进和推广了一些人的最新的结果．
- 公共不动点 /
- 非扩张映象序列 /
- 粘性逼近 /
- 半闭原理 /
- 弱序列连续的对偶映象 /
- 正规对偶映象
Abstract: The purpose is by using the viscosity approximation method to study the cnvergence problem of the iterative scheme for an infinite family of onexpansive mappings and a given contractive mapping in a reflexive Banach space. Under suitable conditions, it was proved that the iterative sequence converges strongly to a common fixed point which was also the unique solution of some variational inequality in a reflexive Banach space. The results presented extend and improve some recent results.
- sequence of nonexpansive mappings /
- viscosity approximation /
- common fixed point /
- demi-closed principle /
- weakly sequentially continuous duality mapping /
- normalized duality mapping

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参考文献(14)

[1]	Bauschke H H.The approximation of fixed points of compositions of nonexpansive mappings in Banach spaces[J].J Math Anal Appl,1996，202：150—159. doi: 10.1006/jmaa.1996.0308
[2]	Browder F E.Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces[J].Arch Rational Mech Anal,1967,24：82—90.
[3]	Chang S S.Viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces[EB].
[4]	Jung J S.Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces[J].J Math Anal Appl,2005,302：509—520. doi: 10.1016/j.jmaa.2004.08.022
[5]	O'Hara J G,Pillay P,Xu H K.Iterative approaches to finding nearest common fixed point of nonexpansive mappings[J].Nonlinear Anal TMA,2003,54：1417—1426. doi: 10.1016/S0362-546X(03)00193-7
[6]	Song Y S,Chen R D,Zhou H Y.Viscosity approximation methods for nonexpansive nonself-mappings[J].J Math Anal Appl,2006,314：701—709. doi: 10.1016/j.jmaa.2005.04.018
[7]	Xu H K.Viscosity approximation methods for nonexpansive mappings[J].J Math Anal Appl,2004,298：279—291. doi: 10.1016/j.jmaa.2004.04.059
[8]	Shioji N,Takahashi W.Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces[J].Proc Amer Math Soc,1997,125：3641—3645. doi: 10.1090/S0002-9939-97-04033-1
[9]	Shimizu T,Takahashi W.Strong convergence to common fixed points of families of nonexpansive mappings[J].J Math Anal Appl,1997,211：71—83. doi: 10.1006/jmaa.1997.5398
[10]	Lim T C,Xu H K.Fixed point theories for asymptotically nonexpansive mappings[J].Nonlinear Anal TMA, 1994,22：1345—1355. doi: 10.1016/0362-546X(94)90116-3
[11]	Goebel K,Kirk W A.Topies in metric fixed point theory[J].Cambridge Studies in Advanced Mathematics,v 28,Cambridge University Press, 1990.
[12]	Chang S S.Some problems and results in the study of nonlinear analysis[J].Nonlinear Anal TMA,1997,30(7)：4197—4208. doi: 10.1016/S0362-546X(97)00388-X
[13]	Liu L S.Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive mappings in Banach spaces[J].J Math Anal Appl,1995,194:114—125. doi: 10.1006/jmaa.1995.1289
[14]	Bruck R E.On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces[J].Israel J Math, 1981,38：304—314. doi: 10.1007/BF02762776