Copyright © 2010 Siwaporn Saewan 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. K. Ball, E. A. Carlen, and E. H. Lieb, “Sharp uniform convexity and smoothness inequalities for trace norms,” Inventiones Mathematicae, vol. 115, no. 3, pp. 463–482, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
2. Y. Takahashi, K. Hashimoto, and M. Kato, “On sharp uniform convexity, smoothness, and strong type, cotype inequalities,” Journal of Nonlinear and Convex Analysis, vol. 3, no. 2, pp. 267–281, 2002. View at Zentralblatt MATH · View at MathSciNet
3. Y. I. Alber and S. Reich, “An iterative method for solving a class of nonlinear operator equations in Banach spaces,” Panamerican Mathematical Journal, vol. 4, no. 2, pp. 39–54, 1994. View at MathSciNet
4. 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 · View at MathSciNet
5. 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 MathSciNet
6. S. Kamimura and W. Takahashi, “Strong convergence of a proximal-type algorithm in a Banach space,” SIAM Journal on Optimization, vol. 13, no. 3, pp. 938–945, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
7. W. Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, Yokohama, Japan, 2000, Fixed Point Theory and Its Application. View at MathSciNet
8. 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 · View at MathSciNet
9. E. Blum and W. Oettli, “From optimization and variational inequalities to equilibrium problems,” The Mathematics Student, vol. 63, no. 1–4, pp. 123–145, 1994. View at Zentralblatt MATH · View at MathSciNet
10. P. L. Combettes and S. A. Hirstoaga, “Equilibrium programming in Hilbert spaces,” Journal of Nonlinear and Convex Analysis, vol. 6, no. 1, pp. 117–136, 2005. View at Zentralblatt MATH · View at MathSciNet
11. A. Moudafi, “Second-order differential proximal methods for equilibrium problems,” Journal of Inequalities in Pure and Applied Mathematics, vol. 4, no. 1, article 18, 7 pages, 2003. View at Zentralblatt MATH · View at MathSciNet
12. S. Reich, “A weak convergence theorem for the alternating method with Bregman distances,” in Theory and Applications of Nonlinear Operators of 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 · View at MathSciNet
13. W. Nilsrakoo and S. Saejung, “Strong convergence to common fixed points of countable relatively quasi-nonexpansive mappings,” Fixed Point Theory and Applications, vol. 2008, Article ID 312454, 19 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
14. Y. Su, D. Wang, and M. Shang, “Strong convergence of monotone hybrid algorithm for hemi-relatively nonexpansive mappings,” Fixed Point Theory and Applications, vol. 2008, Article ID 284613, 8 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
15. H. Zegeye and N. Shahzad, “Strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 7, pp. 2707–2716, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
16. 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 Zentralblatt MATH · View at MathSciNet
17. 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 · View at MathSciNet
18. Y. Censor and S. Reich, “Iterations of paracontractions and firmly nonexpansive operators with applications to feasibility and optimization,” Optimization, vol. 37, no. 4, pp. 323–339, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
19. S. Matsushita and W. Takahashi, “A strong convergence theorem for relatively nonexpansive mappings in a Banach space,” Journal of Approximation Theory, vol. 134, no. 2, pp. 257–266, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
20. H. Iiduka, W. Takahashi, and M. Toyoda, “Approximation of solutions of variational inequalities for monotone mappings,” Panamerican Mathematical Journal, vol. 14, no. 2, pp. 49–61, 2004. View at Zentralblatt MATH · View at MathSciNet
21. H. Iiduka and W. Takahashi, “Weak convergence of a projection algorithm for variational inequalities in a Banach space,” Journal of Mathematical Analysis and Applications, vol. 339, no. 1, pp. 668–679, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
22. S. Matsushita and W. Takahashi, “Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces,” Fixed Point Theory and Applications, vol. 2004, no. 1, pp. 37–47, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
23. W. Takahashi and K. Zembayashi, “Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 1, pp. 45–57, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
24. W. Takahashi and K. Zembayashi, “Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings,” Fixed Point Theory and Applications, vol. 2008, Article ID 528476, 11 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
25. X. Qin and Y. Su, “Strong convergence theorems for relatively nonexpansive mappings in a Banach space,” Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 6, pp. 1958–1965, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
26. L. Wei, Y. J. Cho, and H. Zhou, “A strong convergence theorem for common fixed points of two relatively nonexpansive mappings and its applications,” Journal of Applied Mathematics and Computing, vol. 29, no. 1-2, pp. 95–103, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
27. P. Cholamjiak, “A hybrid iterative scheme for equilibrium problems, variational inequality problems, and fixed point problems in Banach spaces,” Fixed Point Theory and Applications, vol. 2009, Article ID 719360, 18 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
28. P. Kumam and K. Wattanawitoon, “Convergence theorems of a hybrid algorithm for equilibrium problems,” Nonlinear Analysis: Hybrid Systems, vol. 3, no. 4, pp. 386–394, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
29. B. Beauzamy, Introduction to Banach Spaces and Their Geometry, North-Holland, Amsterdam, The Netherlands, 2nd edition, 1995.
30. H. K. Xu, “Inequalities in Banach spaces with applications,” Nonlinear Analysis: Theory, Methods & Applications, vol. 16, no. 12, pp. 1127–1138, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
31. C. Zălinescu, “On uniformly convex functions,” Journal of Mathematical Analysis and Applications, vol. 95, no. 2, pp. 344–374, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
32. R. T. Rockafellar, “On the maximality of sums of nonlinear monotone operators,” Transactions of the American Mathematical Society, vol. 149, pp. 75–88, 1970. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
33. F. Kohsaka and W. Takahashi, “Strong convergence of an iterative sequence for maximal monotone operators in a Banach space,” Abstract and Applied Analysis, no. 3, pp. 239–249, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
34. S. Plubtieng and W. Sriprad, “An extragradient method and proximal point algorithm for inverse strongly monotone operators and maximal monotone operators in Banach spaces,” Fixed Point Theory and Applications, vol. 2009, Article ID 591874, 16 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
35. S. Plubtieng and W. Sriprad, “Strong and weak convergence of modified Mann iteration for new resolvents of maximal monotone operators in Banach spaces,” Abstract and Applied Analysis, vol. 2009, Article ID 795432, 20 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet