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ISHIKAWA ITERATIVE SEQUENCE WITH ERRORS FOR φ-STRONGLY ACCRETIVE OPERATORS

LI, YOUNG-JIN   (Department of Mathematics Sun Yat-sen University  );
  • 초록

    In this paper, the iterative solution is studied for equation Tx = f with a uniformly continuous ${\varphi}$ -strongly accretive operators in arbitrary real Banach spaces. Our results extend, generalize and improve the corresponding results obtained by Zeng [11].


  • 주제어

    Ishikawa iterative sequences with errors .   duality mapping .   Banach space.  

  • 참고문헌 (15)

    1. C. E. Chidume, An approximation method for monotone Lipschitzian operators in Hilbert spaces, J. Aust. Math. Soc.(series A) 41 (1986), 59-63 
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    3. C. E. Chidume, Nonlinear accretive and pseudo-contractive operator equations in Banach spaces, Nonlinear Anal. 31 (1998), 779-789 
    4. C. E. Chidume and H. Zegeye, Approximation of the zeros of m-accretive operator, Nonlinear Anal. 37 (1999), 81-96 
    5. C. E. Chidume, Iterative solution of $0\{in}$ Ax for an m-accretive operator A in certain Banach spaces, J. Math. Anal. Appl. 269 (2002), 421-430 
    6. W. G. Dotson, An iterative process for nonlinear monotonic nonexpansive opera- tors in Hilbert space, Math. Comp. 32 (1978), 223-225 
    7. T. Kato, Nonlinear semigroups and evolutions equations, J. Math. Soc. Japan. 19 (1967), 508-520 
    8. L. Liu, Ishikawa-type and Mann-type iterative process with errors for constructing solutions of nonlinear equations involving m-accretive operators in Banach spaces, Nonlinear Anal. 34 (1998), 307-317 
    9. Z. Q. Liu, Y. G. Xu and Y. J. Cho, Iterative solution of nonlinear equations with $\phi$-strongly accretive operators, Arch. Math. 77 (2001), 508-516 
    10. Z. Luchuan, Ishikawa type iterative sequences with errors for Lipschitzian $\varphi$strongly accretive operator equations in arbitrary Banach spaces, Numer. Math. J. Chinese Univ.(English Ser.) 11 (2002), 25-33 
    11. R. H. Martin, Jr., A global existence theorem for autonomous differential equa- tions in Banach space, Proc. Amer. Math. Soc. 26 (1970), 307-314 
    12. S. Reich, An iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear Anal. 2 (1978), 85-92 
    13. R. T. Rockafellar, Local boundedness of nonlinear, monotone operator, Michigan Math. J. 16 (1969), 397-407 
    14. C. E. Chidume, The iterative solution of the equation f = x + Tx for a monotone operator T in $L^{p}$ space, J. Math. Anal. Appl. 116 (1986), 531-537 
    15. Y. Xu, Ishikawa and Mann Iterative process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), 91-101 

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