留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

m-增生算子方程解的Mann和Ishikawa迭代逼近

张石生

张石生. m-增生算子方程解的Mann和Ishikawa迭代逼近[J]. 应用数学和力学, 1999, 20(12): 1215-1223.
引用本文: 张石生. m-增生算子方程解的Mann和Ishikawa迭代逼近[J]. 应用数学和力学, 1999, 20(12): 1215-1223.
Zhang Shisheng. Mann and Ishikawa Iterative Approximation of Solutions for m-Accretive Operator Equations[J]. Applied Mathematics and Mechanics, 1999, 20(12): 1215-1223.
Citation: Zhang Shisheng. Mann and Ishikawa Iterative Approximation of Solutions for m-Accretive Operator Equations[J]. Applied Mathematics and Mechanics, 1999, 20(12): 1215-1223.

m-增生算子方程解的Mann和Ishikawa迭代逼近

基金项目: 国家自然科学基金(19971058)
详细信息
    作者简介:

    张石生(1934~ ),男,教授,已发表论文270余篇,获省部级奖6项.

  • 中图分类号: O177.91

Mann and Ishikawa Iterative Approximation of Solutions for m-Accretive Operator Equations

  • 摘要: 研究了Banach空间中具m-增生算子的方程解的Mann和Ishikawa迭代逼近问题。研究结果改进和发展了一些文献中的最新成果。
  • [1] Lindehstrauss J, Tsafriri L. Classical Banach Spaces Ⅱ[M]. New York/Berlin: Springer-Verlag,1979.
    [2] Xu Z B, Roach G F. Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces[J]. J Math Anal Appl,1991,157:189~210.
    [3] Browder F E, Nonlinear mappings of nonexpansive and accretive type in Banach spaces[J]. Bull Amer Math Soc,1967,73:875~882.
    [4] Kato T. Nonlinear semigroups and evolution equations[J]. J Math Soc Japan,1967,19:508~520.
    [5] Martin R H, Jr. A global existence theorem for autonomous differential equations in Banach spaces[J]. Proc Amer Math Soc,1970,26:307~314.
    [6] Ishikawa S. Fixed points by a new iterative method[J]. Proc Amer Math Soc,1974,44:147~150.
    [7] Mann W R. Mean value method in iteration[J]. Proc Amer Math Soc,1953,4:506~510.
    [8] Chidume C E. An approximation method for monotone Lipschitzian operators in Hilbert space[J]. J Austral Math Soc,1986,41:59~63.
    [9] Chidume C E. Iterative solution of nonlinear equations of the monotone and dissipative types[J].
    [10] Appl Anal,1989,33:79~86.
    [11] Chidume C E. Iterative solution of nonlinear equations of the monotone type in Banach spaces[J]. Bull Austral Math Soc,1990,42:21~31.
    [12] 邓磊,丁协平,Lipschitz局部严格伪压缩映象的迭代逼近[J].应用数学和力学,1994,15(2):115~119.
    [13] Deng Lei, Ding Xieping. Iterative approximation of Lipschitz strictly pseudo-contractive mappings in uniformly smooth Banach space[J]. Nonlinear Appl,1995,24:981~987.
    [14] Ding Xieping, Deng Lei. Iterative solution of nonlinear equations of the monotone and dissipative types in uniformly smooth Banach spaces[J]. J Sichuan Normal Univ,1994,17(1):43~48.
    [15] Tan K K, Xu H K. Iterative solutions to nonlinear equations of strongly accretive operators in Banach spaces[J]. J Math Anal Appl,1993,178:9~21.
    [16] Chang S S, Cho Y J, Lee B S, et al. Iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces[J]. J Math Anal Appl,1998,224:149~165.
    [17] Chidume C E. Iterative approximation of fixed points of Lipschitzian strictly pseudo-contractive mappings[J]. Proc Amer Math Soc,1987,99:283~288.
    [18] Chidume C E. An iterative process for nonlinear Lipschitzian strongly accretive mappings in Lp spaces[J]. J Math Anal Appl,1990,151:453~461.
    [19] Chidume C E. Approximation of fixed points of strongly pseudo-contractive mappings[J]. Proc Amer Math Soc,1994,120:545~551.
    [20] Zhu L C. Iterative solution of nonlinear equations involving m-accretive operators in Banach spaces[J]. J Math Anal Appl,1994,188:410~415.
    [21] Chidume C E, Osilike M O. Approximation methods for nonlinear operator equations of the m~accretive type[J]. J Math Anal Appl,1995,189:225~239.
    [22] Chang S S, Tan K K. Iteration processes for approximation fixed points of operators of monotone type[J]. Bull Austral Math Soc,1998,57:433~445.
    [23] Liu L S. Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces[J]. J Math Anal Appl,1995,194:114~125.
    [24] Bruck R E. The iterative solution of the equation y∈x+Tx for a monotone operator T in Hilbert space[J]. Bull Amer Math Soc,1973,79:1258~1262.
    [25] Chang S S. Some problems and results in the theory of nonlinear analysis[J]. Nonlinear Analysis TMA,1997,30(7):4197~4208.
    [26] Ding Xieping. Iterative process with errors of nonlinear equations involving m-accretive operators[J]. J Math Anal Appl,1997,209:191~201.
    [27] Zeng Luchuan. Error bounds for approximation solutions to nonlinear equations of strongly accretive operators in uniformly smooth Banach spaces[J]. J Math Anal Appl,1997,209:67~80.
    [28] Barbu V. Nonlinear Semigroups and Differential Equations in Banach Spaces[M]. Leyden: Noordhoff,1976.
    [29] Browder F E. Nonlinear monotone and accretive operators in Banach spaces[J]. Proc Nat Acad Sci U S A,1968,61:388~392.
    [30] Nevanlinna O. Reich S. Strong convergence of contraction semi-groups and of iterative methods for accretive operators in Banach spaces[J]. Israel J Math,1979,32:44~58.
    [31] Osilike M O. Approximation methods for nonlinear m-accretive operator equations[J]. J Math Anal Appl,1997,209:20~24.
    [32] Reich S. An iterative procedure for constructing zeros of accretive sets in Banach spaces[J]. Nonlinear Anal,1978,2:85~92.
    [33] Reich S. Strongly convergence theorems for resolvents of accretive operators in Banach spaces[J]. J Math Anal Appl,1980,75:287~292.
    [34] Weng X. Fixed point iteration for local strictly pseudo-contractive mappings[J]. Proc Amer Math Soc,1991,113:727~731.
    [35] 曾六川. Lipschitz局部强增殖算子的非线性方程的解的迭代构造[J]. 应用数学和力学,1995,16(6):543~552.
  • 加载中
计量
  • 文章访问数:  1679
  • HTML全文浏览量:  58
  • PDF下载量:  684
  • 被引次数: 0
出版历程
  • 收稿日期:  1998-03-27
  • 修回日期:  1999-05-31
  • 刊出日期:  1999-12-15

目录

    /

    返回文章
    返回