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渐近非扩张型映像的黏性三步迭代序列强收敛性 被引量：3

Strong convergence of the viscosity three-step iterative sequences for asymptotic noexpansive mappings
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摘要 在一致凸Banach空间中,研究了渐近非扩张映像不动点的黏性三步迭代法,证明了在一定条件下该迭代序列强收敛于T的不动点,从而改进和推广了近代相关的一些结果. A new viscosity three-step iterative method for the fixed points of asymptotic noexpansive mappings was given in uniformly convex Banach spaces. A strongly convergent theorem for this kind of iterative sequences was obtained. The results extended some recent results in literatures obtained by other authors.
作者 董家帅 王元恒 罗红平
机构地区 浙江师范大学数理与信息工程学院
出处 《浙江师范大学学报（自然科学版）》 CAS 2012年第3期241-245,共5页 Journal of Zhejiang Normal University:Natural Sciences
基金 国家自然科学基金资助项目(11071169) 浙江省自然科学基金资助项目(Y6100696)
关键词 渐近非扩张映像 不动点 三步迭代序列 黏性 asymptotic noexpansive mapping fixed point three-step iterative sequence viscosity
分类号 O177.91 [理学—基础数学]
  • 相关文献

参考文献7

  • 1Xu Benlong,Noor M A. Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces [ J ]. J Math Anal Appl, 2002,267 (2) :444.453.
  • 2高改良,周海云,张文良.Banach空间中一类映像的三重迭代法[J].应用泛函分析学报,2011,13(1):91-94. 被引量：1
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  • 5杨柳,王元恒.修正混合的Halpern三步迭代序列强收敛性[J].南阳师范学院学报,2010,9(6):1-4. 被引量：1
  • 6宣渭峰,王元恒.双复合修正的Ishikawa迭代逼近非扩张映像不动点[J].浙江师范大学学报（自然科学版）,2009,32(4):401-405. 被引量：6
  • 7Song Yisheng. A new sufficient condition for the strong convergence of Halpem type iterations [ J ]. Appl Math Comput,2008,198 ( 2 ) :721-728.

二级参考文献24

  • 1黄建锋,王元恒.关于一种严格伪压缩映象Mann迭代序列的强收敛性[J].浙江师范大学学报（自然科学版）,2006,29(4):378-381. 被引量：4
  • 2姚永红,陈汝栋,周海云.非扩张映象不动点的迭代算法[J].数学学报（中文版）,2007,50(1):139-144. 被引量：6
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  • 7Xu Hongkun. Iterative algorithms for nonlinear operators[ J]. J London Math Soc ,2002,66( 1 ) :240-256.
  • 8Kim T H, Xu Hongkun. Strong convergence of modified Mann iterations [ J ]. Nonlinear Anal,2005,61 ( 2 ) :51-60.
  • 9Suzuki T. Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals[ J]. J Math Anal Appl,2005,305( 1 ) :227-239.
  • 10Yao Y, Chen R, Yao J C. Strong convergence and certain control conditions for modified Mann iteration [ J ]. Nonlinear Anal ,2008,68 : 1687 - 1693.

共引文献5

同被引文献42

  • 1Goebol K, Kirk W A. A fixed point theorem for asymptotically nonexpansive mappings. Proc: Amer. Math. Soc., 1972, 19(1): l71-174.
  • 2Schu J. Iterative construction of fixed points of asymptotically nonexpansive mappings. J. Math. Anal. Appl., 1991, 158: 407-413.
  • 3Chang S S. Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings. Proc. Amer. Math. Soc., 2000, 129(3): 845-853.
  • 4Wang Y H. Strong convergence theorems for asymptotically weak G-pseudo-lji-contractive nonself mappings with the generalized projection in Banach spaces. Abst. Appl. Anal., 2012, doi: 10.1155/2012/651304, Article ID 651304: 1-11.
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  • 6XuHongkun.Viscosityapproximationmethodsfornonexpansivemappings[J].JMathAnalAppl,2004,298(1):279-291.
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  • 8ChenJunmin,ZhangJunmin,FanTiegang.Viscosityapproximationmethodsfornonexpansivemappingsandmonotonemappings[J].JMathAnalAppl,2007,334(2):1450-1461.
  • 9SongYisheng,ChenRudong,ZhouHaiyun.ViscosityapproximationmethodsfornonexpansivemappingsequencesinBanachspaces[J].Non-linearAnal,2007,66(5):1016-1024.
  • 10CengLC,GuuSM,YaoJC.AgeneralcompositeiterativealgorithmfornonexpansivemappingsinHilbertspaces[J].ComputMathAppl,2011,61(9):2447-2455.

引证文献3

二级引证文献12

浙江师范大学学报（自然科学版）
2012年 第3期

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