Iterative process for lipschitz local strictly pseudocontractive mappings

  • Deng Lei
  • Ding Xie-ping


Suppose that K is a non-empty subset of a uniformly smooth Banach space X. Let T:K→X be a Lipschitz local strictly pseudocontractive mapping. In this paper, the iterative sequence which converges strongly to the unique fixed point of T is given. A related result deals with the problem that the Ishikawa iteration process converges strongly to a solution of the equation TX=f wheh T is Lipschitzian and local strongly accretive in X.

Key words

local strictly pseudocontractive local strongly accretive uniformly smooth Banach space 


  1. [1]
    Chidume, C. E., Iterative approximation of fixed points of Lipschitzian strictly pseudocontractive mappings,Proc. Amer. Math. Soc.,99, 2 (1987), 283–288.MATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Deng, L. and X. P. Ding, Iterative approximation of Lipschitz strictly pseudocontractive mappings in uniformly smooth Banach spaces (submitted).Google Scholar
  3. [3]
    Ishikawa, S., Fixed points by a new iteration method,Proc. Amer. Math. Soc.,44 (1974), 147–150.MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Kato, T., Nonlinear semigroups and evolution equations,J. Math. Soc. Japan,19 (1967), 508–520.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Lindenstrauss, J. and L. Tsafriri,Classical Banach Spaces, II, Springer-Verlag, New York/Berlin (1979).MATHGoogle Scholar
  6. [6]
    Reich, S., An iterative procedure for constructing zeros of accretive sets in Banach spaces,J. Nonlinear Anal., 2 (1978), 85–92.MATHCrossRefGoogle Scholar
  7. [7]
    Weng, X., Fixed point iteration for local strictly pseudocontractive mapping,Proc. Amer. Math. Soc.,113 (1991), 727–731.MATHMathSciNetCrossRefGoogle Scholar
  8. [8]
    Xu, Z. B. and G. F. Roach, Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces,J. Math. Anal. Appl.,157 (1991), 189–210.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© SUT 1994

Authors and Affiliations

  • Deng Lei
    • 1
  • Ding Xie-ping
    • 2
  1. 1.Chongqing Teacher’s CollegeChongqing
  2. 2.Sichuan Normal UniversityChengdu

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