Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ITERATIVE APPROXIMATIONS OF ZEROES FOR ACCRETIVE OPERATORS IN BANACH SPACES

  • Cho Yeol-Je (Department of Mathematics and the Research Institute of Natural Sciences Gyeongsang National University) ;
  • Zhou Haiyun (Department of Mathematics Shijiazhuang Mechanical Engineering College) ;
  • Kim Jong-Kyu (Department of Mathematics Kyungnam University)
  • Published : 2006.04.01
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Abstract

In this paper, we introduce and study a new iterative algorithm for approximating zeroes of accretive operators in Banach spaces.

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References

  1. H. Brezis and P. L. Lions, Produits infinis de resolvants, Israel J. Math. 29 (1978), 329-345 https://doi.org/10.1007/BF02761171
  2. F. E. Browder, Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 660-665 https://doi.org/10.1090/S0002-9904-1968-11983-4
  3. R. E. Bruck and G. B. Passty, Almost convergence of the infinite product of resolvents in Banach spaces, Nonlinear Anal. 3 (1979), 279-282 https://doi.org/10.1016/0362-546X(79)90083-X
  4. R. E. Bruck and S. Reich, Nonexpansive projections and resolvents of accretive operators in Banach spaces, Houston J. Math. 3 (1977), 459-470
  5. B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967), 957-961 https://doi.org/10.1090/S0002-9904-1967-11864-0
  6. J. S. Jung and W. Takahashi, Dual convergence theorems for the infinite products of resoluenis in Banach spaces, Kodai Math. J. 14 (1991), 358-364 https://doi.org/10.2996/kmj/1138039461
  7. S. Kamimura, S. H. Khan and W. Takahashi, Iterative schemes for approximating solutions of relations involving accretive operators in Banach spaces, Fixed Point Theory and Applications, Vol. 5, Edited by Y. J. Cho, J. K. Kim and S. M. Kang, Nova Science Publishers, Inc., 2003, 41-52
  8. P. L. Lions, Une methode iterative de resolution d'une inequation variationnelle, Israel J. Math. 31 (1978), 204-208 https://doi.org/10.1007/BF02760552
  9. L. S. Liu, Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995), 114-125 https://doi.org/10.1006/jmaa.1995.1289
  10. W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510
  11. O. Nevanlinna and S. Reich, Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces, Israel J. Math. 32 (1979), 44-58 https://doi.org/10.1007/BF02761184
  12. Z. Opial, Weak convergence of the sequence of successive approximations for non expansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597 https://doi.org/10.1090/S0002-9904-1967-11761-0
  13. A. Pazy, Remarks on nonlinear ergodic theory in Hilbert spaces, Nonlinear Anal. 6 (1979), 863-871
  14. S. Reich, On infinite products of resoluenis, Atti Acad. Naz. Lincei 63 (1977), 338-340
  15. S. Reich, Weak convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 67 (1979), 274-276 https://doi.org/10.1016/0022-247X(79)90024-6
  16. S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980), 287-292 https://doi.org/10.1016/0022-247X(80)90323-6
  17. R. T. Rockafellar , Monotone operators and the proximal point algorithm, SIAM J. Control and Optim. 14 (1976), 877-898 https://doi.org/10.1137/0314056
  18. W. Takahashi, Nonlinear Functional Analysis, Kindai-Kagaku-Sha, Tokyo, 1988
  19. W. Takahashi, Fixed point theorems and nonlinear ergodic theorems for nonlinear semigroups and their applications, Nonlinear Anal. 30 (1997), 1283-1293 https://doi.org/10.1016/S0362-546X(96)00262-3
  20. W. Takahashi, Nonlinear Analysis and Convex Analysis, Edited by W. Takahashi and T. Tanaka, World Scientific Publishing Company, 1999, p. 87-94
  21. W. Takahashi and G. E. Kim, Approximating fixed points of nonexpansive mappings in Banach spaces, Math. Japon. 48 (1998), 1-9
  22. W. Takahashi and Y. Ueda, On Reich's strong convergence theorems for resolve of accretive operators, J. Math. Anal. Appl. 104 (1984), 546-553 https://doi.org/10.1016/0022-247X(84)90019-2