Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

ITERATIVE PROCESS WITH ERRORS FOR m-ACCRETIVE OPERATORS

  • Baek, J.H (Department of Mathematics Gyeongsang National University ) ;
  • Cho, Y.J. (Department of Mathematics Gyeongsang National University ) ;
  • Chang, S.S (Department of Mathematics Sichuan University )
  • Published : 1998.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we prove that the Mann and Ishikawa iteration sequences with errors converge strongly to the unique solution of the equation x + Tx = f, where T is an m-accretive operator in uniformly smooth Banach spaces. Our results extend and improve those of Chidume, Ding, Zhu and others.

Keywords

References

  1. Nonlinear semigroups and Differential Equations in Banach Spaces V. Barbu
  2. Proc. Nat. Acad. Sci. U.S.A. v.61 Nonlinear monotonic and accretive operators in Banach spaces F.E. Browder
  3. Bull. Amer. Math. Soc. v.73 Nonlinear mappings of nonexpansoce and accretive type in Banach spaces F.E. Browder
  4. Bull. Amer. Math. Soc. v.79 The iterative solution of the equation y∈x+Tx for a monotone operator T in Hilbert space R.E. Bruck
  5. Some problems and results in the theory of nonlinear analysis S.S. Chang
  6. Iterationprocesses of fixed points for operators of monotone type in Banach spaces S.S. Chang;K.K Tan
  7. On Chidume's open question and iterative apptoximations of strongly accretive and strongly pseudo-contractive mappings in Banach spaces S.S. Chang;Y. J. Cho;B.S. Lee;S.M. Kang
  8. J. Austral. Math. Soc. v.41 An approximation method for monotone Lipscitzian operator Hilbert space C.E. Chidume
  9. Appl. Anal. v.33 Iterative solution of nonlinear equations of the monotone and dissipative types C.E. Chidume
  10. Bull. Austral. Math. Soc. v.42 Iterative solution of nonlinear equations of the monotone type in Vanach spaces C.E. Chidume
  11. Proc. Amer. Math. Soc. v.99 Iterative approximation of fixed points of Lipschitzian strictly pseudo-contractive mappings C.E. Chidume
  12. J. MAth. Anal. Appl. v.151 An iterative process for nonlinear Lipschitzian strongly pseudo-contractive mappings in $L_p$ C.E. Chidume
  13. Proc. Amer. Math. Soc. v.120 Approximation of fixed points of strongly pseudo-contractive mappings C.E. Chidume
  14. J. Math. Anal. Appl. v.189 Approximation methods for nonlinear operator equations of the m-accretive type C.E. Chidume;M.O. Osilike
  15. Appl. Math. Mech. v.15 Iterative process for Lipscitiz local strictly pseudo-contractive mappings L. Deng;X. P. Ding
  16. Nonlinear Appl. v.24 Iterative approximation of Lopschitz strictly pseudo-contractive mappings in uniformly smooth Banach spaces L. Deng;X.P. Ding
  17. J. Math. Anal. Appl. v.209 Iterative process with errors of nonlinear equations involving maccretive operators X.P. Ding
  18. J. Sichuan Normal Univ. v.17 Iterative solution of nonlinear equations of the monotone and dissipative types in uniformly smooth Banach spaces X.P. Ding;L. Deng
  19. Proc. Amer. Math. Soc. v.44 Fixed points by a new iterative method S. Ishikawa
  20. J. Math. Soc. Japan v.19 Nonlinear semigroups and evolution equations T. Kato
  21. Classical Banach Spaces Ⅱ J. Lindehstrauss;L. Tsafriri
  22. J. Math. Anal. Appl. v.194 Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces L.S Liu
  23. Proc. Amer. Math. Soc. v.4 Mean value method in iteration W.R. Mann
  24. Proc. Amer. Math. Soc. v.26 A global existence theorem for autonomous differential equations in Banach spaces R.H. Martin
  25. Israel J. Math. v.32 Strong convergence of constraction semi-geoups and of iterative methods for accretive operators in Banach spaces O. Nevanlinna;S. Reich
  26. J. Math. Anal. Appl. v.209 Approximation methods for nonlinear m-accretive operator equations M.O. Osilike
  27. Nonlinear Anal. v.2 An iterative procedure for constructing zeros of accretive sets in Banach spaces S. Reich
  28. J. Math. Anal. Appl. v.75 Strongly convergence theroems for resolvents of accretive operators in Vanach spaces S. Reich
  29. J. Math. Anal. Appl. v.178 Iterative solutions to nonlinear equations of strongly accretive operators in Banach spaces K.K Tan;H.K. Xu
  30. Proc. Amer. Math. Soc. v.113 Fixed point iteration for local strictly pseudo-contractive mappings X. Weng
  31. J. MAth. Anal. Appl. v.157 Characteristics inequalities of uniformly convex and uniformly smooth Banach spaces Z.B. Xu;G.F. Roach
  32. Appl. Math. Mech. v.16 Iterative construction of solutions to nonlinear equations of Lipschitzian and local strongly accretive operators L.C. Zeng
  33. J. Math. Anal. Appl. v.209 Error bounds for approximation solutions to nonlinear equations of strongly accretive operators in uniformly smooth Banach spaces L.C. Zeng
  34. J. Math. Anal. Appl. v.188 Iterative solution of nonlinear equations involving m-accretive operators in Banach spaces L.C. Zhu