Noor Iterations with Error for Non-Lipschitzian Mappings in Banach Spaces

  • 투고 : 2004.10.19
  • 발행 : 2006.06.23

초록

Suppose C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T : $C{\rightarrow}C$ be an asymptotically nonexpansive in the intermediate sense mapping. In this paper we introduced the three-step iterative sequence for such map with error members. Moreover, we prove that, if T is completely continuous then the our iterative sequence converges strongly to a fixed point of T.

키워드

참고문헌

  1. R. E. Bruck, T. Kuczumow and S. Reich, Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform opial property, Colloq. Math., 65(1993), 169-179.
  2. R. Glowinski and P. Le Tallec, "Augemented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics" Siam, Philadelphia, (1989).
  3. K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35(1972), 171-174. https://doi.org/10.1090/S0002-9939-1972-0298500-3
  4. S. Haubruge, V. H Nguyen, and J. J Strodiot, Convergence analysis and applications of the GlowinskiLe Tallec splitting method for .nding a zero of the sum of two maximal monotone operaors, J. Optim. Theory Appl., 97(1998), 645-673. https://doi.org/10.1023/A:1022646327085
  5. J. U. Jeong, M. Aslam Noor and A. Rafiq, Noor iterations for nonlinear Lipschitzian strongly accretive mappings, J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math., 11(4)(2004), 339-350.
  6. G. E. Kim and T. H. Kim, Mann and Ishikawa iterationss with errors for non- Lipschitzian mappings in Banach spaces, Comp. and Math. Appl., 42(2001), 1565- 1570. https://doi.org/10.1016/S0898-1221(01)00262-0
  7. Q. Liu, Iteration sequence for asymptotically quasi-nonexpansive mapping with an error member, J. Math. Anal. Appl., 259(2001), 18-24. https://doi.org/10.1006/jmaa.2000.7353
  8. M. Aslam Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl., 251(2000), 217-229. https://doi.org/10.1006/jmaa.2000.7042
  9. M. Aslam Noor, Three-step iterative algorithms for multivalued quasi variational inclusions, J. Math. Anal. Appl., 255(2001).
  10. M. Aslam Noor, T. M. Rassias and Z. Huang Three-step iterations for nonlinear accretive operator equations, J. Math. Anal. Appl., 274(2002), 59-68. https://doi.org/10.1016/S0022-247X(02)00224-X
  11. R. E. Rhoades and S. M. Soltuz, The equivalence between Mann- Ishikawa Iterations and multistep iteration, Nonlinear Analysis, 58(2004), 219-228. https://doi.org/10.1016/j.na.2003.11.013
  12. J. Schauder, Der Fixpunktsatz in Funktionalraumen, Studia. Math., 2(1930), 171-180.
  13. J. Schu, Iterative construction of fixed points of strictly quasicontractive mapping, Appl. Anal., 40(1991), 67-72. https://doi.org/10.1080/00036819108839994
  14. B. Xu and M. Aslam Noor, Fixed-Point Iterations for Asymptotically Nonexpansive Mappings in Banach Spaces, J. Math. Anal. Appl., 267(2002), 444-453. https://doi.org/10.1006/jmaa.2001.7649