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Hilbert空间中非扩张映象的最近的公共不动点的逼近问题 被引量：2

On the Problem of Nearest Common Fixed Point of Nonexpansive Mappings
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摘要 本文在Hilbert空间的框架下,研究无限族非扩张映象T_1,T_2,…的迭代程序x_n+1=λ_(n+1)y+(1-λ_(n+1))T_(n+1)x_n的收敛性问题．在适当的条件下,证明了该迭代序列收敛于这一非扩张映象族的最近的公共不动点．其结果改进和推广了引文中相应的结果． The purpose of this paper is to study the convergence problem of the iteration scheme xn＋1=λn＋1y＋（1-λn＋1）Tn＋1xn for a family of infinitely many nonexpansive mappings T1, T2 in a Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings. The results presented in this paper extend and improve the corresponding results.
作者 张石生 李向荣 陈志坚
机构地区 宜宾学院数学系 香港理工大学应用数学系
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2006年第6期1297-1302,共6页 Acta Mathematica Sinica：Chinese Series
关键词 公共不动点 非扩张映象 最近点投影 common fixed point the family of nonexpansive mappings nearest pointprojection
分类号 O177.91 [理学—基础数学]
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参考文献13

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同被引文献21

  • 1姚永红,陈汝栋.逼近一致凸Banach空间中渐近非扩张映象的不动点[J].纯粹数学与应用数学,2006,22(2):263-270. 被引量：2
  • 2Geobel K, Kirk W A. A fixed point theorem for asymptotically nonexpansive mappings[J]. Proc. Amer. Math. Soc., 1972,35(1):171-174.
  • 3Shimizu T, Takahashi W. Strong convergence to common fixed points of families of nonexpansive mappings[J]. J. Math. Anal. Appl., 1997,211:71-83.
  • 4Shioji N, Takahashi W. Strong convergence theorems for continuous semigroups in Banach spaces[J]. Math. Japonica, 1999,1:57-66.
  • 5Shioji N, Takahashi W. Strong convergence theorems for asymptotically nonexpansive mappings in Hilbert spaces[J], nonlinear Anal., 1998,34:87-99.
  • 6Suzuki T. On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces[J]. Proc. Amer. Math. Soc., 2002,131:2133-2136.
  • 7Xu H K. A strong convergence theorem for contraction semigroups in Banach spaces[J]. Bull. Aust. Math. Soc., 2005,72: 371-379.
  • 8Chidume C E, Li J, Udomene A. Convergence of paths and approximation of fixed points of asymptotically nonexpansive mappings[J]. Proc. Amer. Math. Soc., 2005,133:473-480.
  • 9Lim T C, Xu H K. Fixed point theorems for asymptotically nonexpansive mappings[J]. Nonlinear Anal., 1994,22:1345-1355.
  • 10Chang S S. Some problems and results in the study of nonlinear analysis[J]. Nonlinear Anal., 1997,30(7):4197- 4208.

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数学学报（中文版）
2006年 第6期

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