East Asian mathematical journal

  • 제26권1호
  • /
  • Pages.81-93
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  • 2010
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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CONVERGENCE THEOREMS OF MULTI-STEP ITERATIVE SCHEMES WITH ERRORS FOR ASYMPTOTICALLY QUASI-NONEXPANSIVE TYPE NONSELF MAPPINGS

  • Kim, Jong-Kyu (DEPARTMENT MATHEMATICS EDUCATION KYUNGNAM UNIVERSITY) ;
  • Saluja, G.S. (DEPARTMENT OF MATHEMATICS & INFORMATION TECHNOLOGY) ;
  • Nashine, H.K. (DEPARTMENT OF MATHEMATICS DISHA INSTITUTE OF MANAGEMENT AND TECHNOLOGY)
  • 투고 : 2009.10.30
  • 심사 : 2010.01.04
  • 발행 : 2010.01.31
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초록

In this paper, a strong convergence theorem of multi-step iterative schemes with errors for asymptotically quasi-nonexpansive type nonself mappings is established in a real uniformly convex Banach space. Our results extend the corresponding results of Wangkeeree [12], Xu and Noor [13], Kim et al.[1,6,7] and many others.

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과제정보

연구 과제 주관 기관 : National Research Foundation of Korea

참고문헌

  1. S. S. Chang, J. K. Kim and S. M. Kang, Approximating fixed points of asymptotically quasi-nonexpansive type mappings by the Ishikawa iterative sequences with mixed errors, Dynamic Systems and Appl., 13(2) (2004), 179-186.
  2. C. E. Chidume, E. U. Ofoedu and H. Zegeye, Strong and weak convergence theorem for asymptotically nonexpansive mappings, J. Math. Anal. Appl., 280 (2003), 364-374. https://doi.org/10.1016/S0022-247X(03)00061-1
  3. R. Glowinski and P. Le Tallec, Augemented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics, Siam Philadelphia, 1989.
  4. K. Goebel and W. A. Kirk, A xed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171-174. https://doi.org/10.1090/S0002-9939-1972-0298500-3
  5. S. Haubruge, V. H. Nguyen and J. J. Strodiot, Convergence analysis and applications of the Glowinski Le Tallec splitting method for finding a zero of the sum of two maximal monotone operators, J. Optim. Theory Appl., 97 (1998), 645-673. https://doi.org/10.1023/A:1022646327085
  6. J. K. Kim, K. H. Kim and K. S. Kim, Convergence theorems of modified three-step iterative sequences with mixed errors for asymptotically quasi-nonexpansive mappings in Banach spaces, Pan American Math. Jour., 14(1) (2004), 45-54.
  7. J. K. Kim, Y. M. Nam and J. Y. Sim, Convergence theorems of implicit iterative sequences for a finite family of asymptotically quasi-nonexpansive type mappings, Nonlinear Analysis TMA, 71 (2009), 2839-2848. https://doi.org/10.1016/j.na.2009.06.090
  8. M. A. Noor, New approximation scheme for general variational inequalities, J. Math.Anal. Appl., 251 (2000), 217-229. https://doi.org/10.1006/jmaa.2000.7042
  9. M. A. Noor, Three-step iterative algorithms for multivalued quasi variational inclusions, J. Math. Anal. Appl., 255 (2001).
  10. G. S. Saluja, Strong convergence theorems of three step iterative sequences with errors for asymptotically quasi-nonexpansive type nonself mappings, J. Advances Appl. Math., Anal. 2 (2007), No.1, 57-69.
  11. K. K. Tan and H. K. Xu, Approximating fixed points of nonexpansive mappings, J. Math. Anal. Appl., 178 (1993), 301-308. https://doi.org/10.1006/jmaa.1993.1309
  12. R. Wangkeeree, Strong convergence theorems of three step iterations with errors for asymptotically quasi-nonexpansive nonself-mappings in Banach spaces, Thai J. Math., 2 (2004), 283-294.
  13. B. L. Xu and M. A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 267 (2002), No.2, 444-453. https://doi.org/10.1006/jmaa.2001.7649