Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces
Volume 2017 (2017), Article ID 5306802, 11 pages
https://doi.org/10.1155/2017/5306802
Research Article

Weak and Strong Convergence Theorems for the Multiple-Set Split Equality Common Fixed-Point Problems of Demicontractive Mappings

1Department of Mathematics, Shaoxing University, Shaoxing 312000, China
2Department of Applied Mathematics, College of Natural Sciences, Pukyong National University, Busan 48513, Republic of Korea

Correspondence should be addressed to Tae-Hwa Kim

Received 29 March 2017; Accepted 19 October 2017; Published 24 December 2017

Academic Editor: Xinguang Zhang

Copyright © 2017 Yaqin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. Y. Censor and T. Elfving, “A multiprojection algorithm using Bregman projections in a product space,” Numerical Algorithms, vol. 8, no. 2-4, pp. 221–239, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. C. Byrne, “Iterative oblique projection onto convex sets and the split feasibility problem,” Inverse Problems, vol. 18, no. 2, pp. 441–453, 2002. View at Publisher · View at Google Scholar · View at Scopus
  3. Y. Yao, R. P. Agarwal, M. Postolache, and Y.-C. Liou, “Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem,” Fixed Point Theory and Applications, vol. 2014, no. 1, article no. 183, 14 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  4. Y. Yao, M. Postolache, and Y.-C. Liou, “Strong convergence of a self-adaptive method for the split feasibility problem,” Fixed Point Theory and Applications, vol. 2013, article no. 201, 12 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  5. Y. Yao, W. Jigang, and Y.-C. Liou, “Regularized methods for the split feasibility problem,” Abstract and Applied Analysis, vol. 2012, Article ID 140679, 13 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  6. A. Moudafi and E. Al-Shemas, “Simultaneous iterative methods for split equality problem,” Transactions on Mathematical Programming and Applications, vol. 1, no. 2, pp. 1–11, 2013. View at Google Scholar
  7. J. Zhao, “Solving split equality fixed-point problem of quasi-nonexpansive mappings without prior knowledge of operators norms,” Optimization. A Journal of Mathematical Programming and Operations Research, vol. 64, no. 12, pp. 2619–2630, 2015. View at Publisher · View at Google Scholar · View at Scopus
  8. J. Zhao and S. Wang, “Mixed iterative algorithms for the multiple-set split equality common fixed-point problems without prior knowledge of operator norms,” Optimization. A Journal of Mathematical Programming and Operations Research, vol. 65, no. 5, pp. 1069–1083, 2016. View at Publisher · View at Google Scholar · View at Scopus
  9. Y. Wang and T. H. Kim, “Simultaneous iterative algorithm for the split equality fixed-point problem of demicontractive mappings,” Journal of Nonlinear Sciences and Applications, vol. 10, no. 1, pp. 154–165, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  10. W. Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, Yokohama, Japan, 2000. View at MathSciNet
  11. G. Marino and H.-K. Xu, “Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 336–346, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. Y. Censor and A. Segal, “The split common fixed point problem for directed operators,” Journal of Convex Analysis, vol. 16, no. 2, pp. 587–600, 2009. View at Google Scholar · View at MathSciNet · View at Scopus
  13. K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, vol. 28 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  14. C. Martinez-Yanes and H.-K. Xu, “Strong convergence of the CQ method for fixed point iteration processes,” Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal, vol. 64, no. 11, pp. 2400–2411, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  15. A. Moudafi, “The split common fixed-point problem for demicontractive mappings,” Inverse Problems, vol. 26, no. 5, Article ID 055007, pp. 587–600, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. M. C. Joshi and R. K. Bose, Some topics in nonlinear functional analysis, John Wiley and Sons, New York, NY, USA, 1985.
  17. P. L. Combettes, Fejér-Monotonicity in Convex Optimization, in Encyclopedia of Optimization, C. A. Floudas and P. M. Pardalos, Eds., vol. 2, Springer-Verlag, New York, NY, USA, 2001.
  18. S.-W. Han and T.-H. Kim, “ϕ-Fejér-monotone sequences and their convergence theorems,” Journal of Nonlinear and Convex Analysis, vol. 17, no. 2, pp. 211–223, 2016. View at Google Scholar · View at MathSciNet
  19. P.-E. Maingé, “Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization,” Set-Valued and Variational Analysis, vol. 16, no. 7-8, pp. 899–912, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. H.-K. Xu, “Iterative algorithms for nonlinear operators,” Journal Of The London Mathematical Society-Second Series, vol. 66, no. 1, pp. 240–256, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. Y. Wang, T.-H. Kim, X. Fang, and H. He, “The split common fixed-point problem for demicontractive mappings and quasi-nonexpansive mappings,” Journal of Nonlinear Sciences and Applications, vol. 10, no. 6, pp. 2976–2985, 2017. View at Publisher · View at Google Scholar · View at MathSciNet