DOI QR코드

DOI QR Code

A CYCLIC AND SIMULTANEOUS ITERATIVE ALGORITHM FOR THE MULTIPLE SPLIT COMMON FIXED POINT PROBLEM OF DEMICONTRACTIVE MAPPINGS

  • Tang, Yu-Chao (Department of Mathematics NanChang University, School of Mathematics and Statistics Xi'an Jiaotong University) ;
  • Peng, Ji-Gen (School of Mathematics and Statistics Xi'an Jiaotong University) ;
  • Liu, Li-Wei (Department of Mathematics NanChang University)
  • 투고 : 2013.08.27
  • 발행 : 2014.09.30

초록

The purpose of this paper is to address the multiple split common fixed point problem. We present two different methods to approximate a solution of the problem. One is cyclic iteration method; the other is simultaneous iteration method. Under appropriate assumptions on the operators and iterative parameters, we prove both the proposed algorithms converge to the solution of the multiple split common fixed point problem. Our results generalize and improve some known results in the literatures.

키워드

참고문헌

  1. H. H. Bauschke and J. M. Borwein, On projection algorithms for solving convex feasi-bility problems, SIAM Rev. 38 (1996), no. 3, 367-426. https://doi.org/10.1137/S0036144593251710
  2. H. H. Bauschke and P. L. Combettes, A weak-to-strong convergence principle for Fejer-monotone methods in Hilbert spaces, Math. Oper. Res. 26 (2001), no. 2, 248-264. https://doi.org/10.1287/moor.26.2.248.10558
  3. H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, New York, 2011.
  4. C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems 18 (2002), no. 2, 441-453. https://doi.org/10.1088/0266-5611/18/2/310
  5. Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms 8 (1994), no. 2-4, 221-239. https://doi.org/10.1007/BF02142692
  6. Y. Censor, T. Elfving, N. Kopf, and T. Bortfeld, The multiple-sets split feasibility prob-lem and its applications for inverse problems, Inverse Problems 21 (2005), no. 6, 2071-2084. https://doi.org/10.1088/0266-5611/21/6/017
  7. Y. Censor, A. Motova, and A. Segal, Perturbed projections and subgradient projections for the multiple-sets split feasibility problem, J. Math. Anal. Appl. 327 (2007), no. 2, 1244-1256. https://doi.org/10.1016/j.jmaa.2006.05.010
  8. Y. Censor and A. Segal, The split common fixed point problem for directed operators, J. Convex Anal. 16 (2009), no. 2, 587-600.
  9. A. Moudafi, The split common fixed point problem for demicontractive mappings, Inverse Problems 26 (2010), no. 5, 055007, 6 pp.
  10. A. Moudafi, A note on the split common fixed-point problem for quasi-nonexpansive operators, Nonlinear Anal. 74 (2011), no. 12, 4083-4087. https://doi.org/10.1016/j.na.2011.03.041
  11. B. Qu and N. Xiu, A note on the CQ algorithm for the split feasibility problem, Inverse Problems 21 (2005), no. 5, 1655-1665. https://doi.org/10.1088/0266-5611/21/5/009
  12. Y. C. Tang, J. G. Peng, and L. W. Liu, A cyclic algorithm for the split common fixed point problem of demicontractive mappings in Hilbert spaces, Math. Modell. Anal. 17 (2012), no. 4, 457-466. https://doi.org/10.3846/13926292.2012.706236
  13. F. Wang and H. K. Xu, Approximating curve and strong convergence of the CQ Algo-rithm for the split feasibility problem, J. Inequal. Appl. 2010 (2010), Article ID 102085, 13 pages.
  14. F. Wang and H. K. Xu, Cyclic algorithms for split feasibility problems in Hilbert spaces, Nonlinear Anal. 74 (2011), no. 12, 4105-4111. https://doi.org/10.1016/j.na.2011.03.044
  15. Z. W. Wang, Q. Z. Yang, and Y. N. Yang, The relaxed inexact projection methods for the split feasibility problem, Appl. Math. Comput. 217 (2011), no. 12, 5347-359. https://doi.org/10.1016/j.amc.2010.11.058
  16. H. K. Xu, A variable Krasnoselskii-Mann algorithm and the multiple-set split feasibility problem, Inverse Problems 22 (2006), no. 6, 2021-2034. https://doi.org/10.1088/0266-5611/22/6/007
  17. H. K. Xu, Iterative methods for the split feasibility problem in infinite dimensional Hilbert spaces, Inverse Problems 26 (2010), no. 10, 105018, 17 pp.
  18. Q. Yang, The relaxed CQ algorithm solving the split feasibility problem, Inverse Problems 20 (2004), no. 4, 1261-1266. https://doi.org/10.1088/0266-5611/20/4/014
  19. Q. Yang and J. Zhao, Generalized KM theorems and their applications, Inverse Problems 22 (2006), no. 3, 833-844. https://doi.org/10.1088/0266-5611/22/3/006
  20. H. Y. Zhang and Y. J. Wang, A new CQ method for solving split feasibility problem, Front. Math. China 5 (2010), no. 1, 37-46. https://doi.org/10.1007/s11464-009-0047-z
  21. J. Zhao and Q. Yang, Several solution methods for the split feasibility problem, Inverse Problems 21 (2005), no. 5, 1791-1799. https://doi.org/10.1088/0266-5611/21/5/017

피인용 문헌

  1. The split common fixed point problem for multivalued demicontractive mappings and its applications pp.1579-1505, 2018, https://doi.org/10.1007/s13398-018-0496-x