Applied Mathematics and Mechanics

, Volume 16, Issue 6, pp 583–592 | Cite as

Iterative construction of solutions to nonlinear equations of lipschitzian and local strongly accretive operators

  • Zeng Luchuan


In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. Let T: X→X be a Lipschitzian and local strongly accretive operator and the set sol(T) of solutions of the equation Tx=f be nonempty. We show that sol(T) is a singleton and the Ishikawa sequence converges strongly to the unique solution of the equation Tx=f. In addition, whenever T is a Lipschitzian and local pseudocontractive mapping from a nonempty convex subset K of X and the set F(T) of fixed points of T is nonempty, we prove that F(T) is a singleton and the Ishikawa sequence converges strongly to the unique fixed point of T. Our results are the improvements and extension of the results of Deng and Ding(4) and Tan and Xu(5).

Key words

local strongly accretive local strictly pseudocontractive p-uniformly smooth Banach space 


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Copyright information

© Shanghai University of Technology (SUT) 1995

Authors and Affiliations

  • Zeng Luchuan
    • 1
  1. 1.Department of MathematicsShanghai Normal UniversityShanghaiP. R. China

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