Copyright © 2012 Xiaolong Qin and Lin Wang. 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. P. L. Combettes, “The convex feasibility problem in image recovery,” in Advanced in Imaging and Electron Physcis, P. Hawkes, Ed., vol. 95, pp. 155–270, Academic Press, New York, NY, USA, 1996.
2. R. Dautray and J. L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, vol. 1–6, Springer, New York, NY, USA, 1988–1993.
3. H. O. Fattorini, Infinite-Dimensional Optimization and Control Theory, vol. 62 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, UK, 1999. View at Zentralblatt MATH
4. M. A. Khan and N. C. Yannelis, Equilibrium Theory in Infinite Dimensional Spaces, Springer, New York, NY, USA, 1991.
5. F. E. Browder, “Nonexpansive nonlinear operators in a Banach space,” Proceedings of the National Academy of Sciences of the United States of America, vol. 54, pp. 1041–1044, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
6. W. A. Kirk, “A fixed point theorem for mappings which do not increase distances,” The American Mathematical Monthly, vol. 72, pp. 1004–1006, 1965. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
7. K. Goebel and W. A. Kirk, “A fixed point theorem for asymptotically nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 35, pp. 171–174, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
8. H. K. Xu, “Existence and convergence for fixed points of mappings of asymptotically nonexpansive type,” Nonlinear Analysis. Theory, Methods & Applications, vol. 16, no. 12, pp. 1139–1146, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
9. L. E. J. Brouwer, “Über Abbildung von Mannigfaltigkeiten,” Mathematische Annalen, vol. 71, no. 1, pp. 97–115, 1912. View at Publisher · View at Google Scholar
10. J. Schauder, “Der Fixpunktsatz in Funktionalraumen,” Studia Mathematica, vol. 2, pp. 171–180, 1930.
11. A. Tychonoff, “Ein Fixpunktsatz,” Mathematische Annalen, vol. 111, no. 1, pp. 767–776, 1935. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
12. E. Casini and E. Maluta, “Fixed points of uniformly Lipschitzian mappings in spaces with uniformly normal structure,” Nonlinear Analysis. Theory, Methods & Applications, vol. 9, no. 1, pp. 103–108, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
13. K. Deimling, “Zeros of accretive operators,” Manuscripta Mathematica, vol. 13, pp. 365–374, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
14. A. Vanderluge, Optical Signal Processing, Wiley, New York, NY, USA, 1992.
15. H. H. Bauschke and J. M. Borwein, “On projection algorithms for solving convex feasibility problems,” SIAM Review, vol. 38, no. 3, pp. 367–426, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
16. C. Byrne, “A unified treatment of some iterative algorithms in signal processing and image reconstruction,” Inverse Problems, vol. 20, no. 1, pp. 103–120, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
17. W. G. Dotson, Jr., “Fixed points of quasi-nonexpansive mappings,” Australian Mathematical Society A, vol. 13, pp. 167–170, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
18. R. Bruck, T. Kuczumow, and S. Reich, “Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property,” Colloquium Mathematicum, vol. 65, no. 2, pp. 169–179, 1993. View at Zentralblatt MATH
19. I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, vol. 62 of Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1990. View at Publisher · View at Google Scholar
20. Y. I. Alber, “Metric and generalized projection operators in Banach spaces: properties and applications,” in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, vol. 178 of Lecture Notes in Pure and Applied Mathematics, pp. 15–50, Marcel Dekker, New York, NY, USA, 1996. View at Zentralblatt MATH
21. H. Hudzik, W. Kowalewski, and G. Lewicki, “Approximate compactness and full rotundity in Musielak-Orlicz spaces and Lorentz-Orlicz spaces,” Zeitschrift für Analysis und ihre Anwendungen, vol. 25, no. 2, pp. 163–192, 2006. View at Publisher · View at Google Scholar
22. S. Reich, “A weak convergence theorem for the alternating method with Bregman distances,” in Theory and Applicationsof Nonlinear Operatorsof Accretive and Monotone Type, vol. 178 of Lecture Notes in Pure and Applied Mathematics, pp. 313–318, Marcel Dekker, New York, NY, USA, 1996. View at Zentralblatt MATH
23. D. Butnariu, S. Reich, and A. J. Zaslavski, “Asymptotic behavior of relatively nonexpansive operators in Banach spaces,” Journal of Applied Analysis, vol. 7, no. 2, pp. 151–174, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
24. D. Butnariu, S. Reich, and A. J. Zaslavski, “Weak convergence of orbits of nonlinear operators in reflexive Banach spaces,” Numerical Functional Analysis and Optimization, vol. 24, no. 5-6, pp. 489–508, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
25. Y. Su and X. Qin, “Strong convergence of modified Ishikawa iterations for nonlinear mappings,” Proceedings of the Indian Academy of Science, vol. 117, no. 1, pp. 97–107, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
26. R. P. Agarwal, Y. J. Cho, and X. Qin, “Generalized projection algorithms for nonlinear operators,” Numerical Functional Analysis and Optimization, vol. 28, no. 11-12, pp. 1197–1215, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
27. X. Qin, Y. Su, C. Wu, and K. Liu, “Strong convergence theorems for nonlinear operators in Banach spaces,” Communications on Applied Nonlinear Analysis, vol. 14, no. 3, pp. 35–50, 2007. View at Zentralblatt MATH
28. H. Zhou, G. Gao, and B. Tan, “Convergence theorems of a modified hybrid algorithm for a family of quasi-$\phi$-asymptotically nonexpansive mappings,” Journal of Applied Mathematics and Computing, vol. 32, no. 2, pp. 453–464, 2010. View at Publisher · View at Google Scholar
29. X. Qin, S. Y. Cho, and S. M. Kang, “On hybrid projection methods for asymptotically quasi-$\phi$-nonexpansive mappings,” Applied Mathematics and Computation, vol. 215, no. 11, pp. 3874–3883, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
30. X. Qin and R. P. Agarwal, “Shrinking projection methods for a pair of asymptotically quasi-$\phi$-nonexpansive mappings,” Numerical Functional Analysis and Optimization, vol. 31, no. 7-9, pp. 1072–1089, 2010. View at Publisher · View at Google Scholar
31. X. Qin, S. Huang, and T. Wang, “On the convergence of hybrid projection algorithms for asymptotically quasi-$\phi$-nonexpansive mappings,” Computers & Mathematics with Applications, vol. 61, no. 4, pp. 851–859, 2011. View at Publisher · View at Google Scholar
32. X. Qin, Y. J. Cho, and S. M. Kang, “Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces,” Journal of Computational and Applied Mathematics, vol. 225, no. 1, pp. 20–30, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
33. X. Qin, Y. J. Cho, S. M. Kang, and H. Zhou, “Convergence of a modified Halpern-type iteration algorithm for quasi-$\phi$-nonexpansive mappings,” Applied Mathematics Letters, vol. 22, no. 7, pp. 1051–1055, 2009. View at Publisher · View at Google Scholar