ZHANG Shi-sheng. Some Convergence Problem of Iterative Sequences for Accretive and Pseudo-Contractive Type Mappings in Banach Spaces[J]. Applied Mathematics and Mechanics, 2002, 23(4): 359-370.
Citation: ZHANG Shi-sheng. Some Convergence Problem of Iterative Sequences for Accretive and Pseudo-Contractive Type Mappings in Banach Spaces[J]. Applied Mathematics and Mechanics, 2002, 23(4): 359-370.

Some Convergence Problem of Iterative Sequences for Accretive and Pseudo-Contractive Type Mappings in Banach Spaces

  • Received Date: 2000-12-12
  • Rev Recd Date: 2001-11-05
  • Publish Date: 2002-04-15
  • Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mappings in Banach spaces were obtained. The results improve, extend and include some recent results.
  • loading
  • [1]
    Browder F E.Nonlinear mappings of nonexpansive and accretive type in Banach spaces[J].Bull Amer Math Soc,1967,73:875-882.
    [2]
    Deimling K.Zeros of accretive mapping[J].Manuscripta Math,1974,13:365-374.
    [3]
    Martin R H.A global existence theorem for autonomous differential equations in Banach spaces[J].Proc Amer Math Soc,1970,26:307-314.
    [4]
    CHANG Shih-sen.On Chidume's open questions and approximate solutions of multivalued strongly accrettive mapping equations in Banach spaces[J].J Math Anal Appl,1997,216:94-111.
    [5]
    CHANG Shih-sen.Some problems and results in the study of nonlinear analysis[J].Nonlinear Anal TMA,1997,30:4197-4208.
    [6]
    CHANG Shih-sen,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.
    [7]
    Chidume C E.Steepest descent approximations for accretive operator equations[J].Nonlinear Anal,TMA,1996,26:299-311.
    [8]
    Chidume C E,Osilike M O.Nonlinear accretive and pseudo-contractive operator equations in Banach spaces[J].Nonlinear Anal,TMA,1998,31:779-789.
    [9]
    Chidume C E.Iterative solutions of nonlinear equations with strongly accretive operators[J].J Math Anal Appl,1995,192:502-518.
    [10]
    Chidume C E.Global iteration schemes for strongly pseudo-contractive maps[J].Proc Amer Math Soc,1998,126(9):2614-2649.
    [11]
    Deng L,Ding X P.Iterative approximation of Lipschitz strictly pseudo-contractive mappings in uniformly smooth Banach spaces[J].Nonlinear Anal,TMA,1995,24:981-987.
    [12]
    Liu L W.Approximation of fixed points of a strongly pseudo-contractive mappings[J].Proc Amer Math Soc,1997,125:1363-1366.
    [13]
    Tan K K,Xu H K.Iterative solution to nonlinear equations and strongly accretive operators in Banach spaces[J].J Math Anal Appl,1993,178:9-21.
    [14]
    Xu Z B,Roach G F.A necessary and sufficient condition for convergence of streepest descent approximation to accretive operator equations[J].J Math Anal Appl,1992,167:340-354.
    [15]
    Zhou H Y,Jia Y T.Approximation of fixed points of strongly pseudo-contractive maps without Lipschitz assumption[J].Proc Amer Math Soc,1997,125:1705-1709.
    [16]
    Fitzpatrick P M,Hess P,Kato T.Local boundedness of monotone type operators[J].Proc Japan Acad,1972,48:275-277.
    [17]
    Kato T.Nonlinear semigroups and evolution equations[J].J Math Soc Japan,1967,19:508-520.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1904) PDF downloads(728) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return