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Linked References

1. F. E. Browder and W. V. Petryshyn, “Construction of fixed points of nonlinear mappings in Hilbert space,” Journal of Mathematical Analysis and Applications, vol. 20, pp. 197–228, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
2. Q. Liu, “Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings,” Nonlinear Analysis, vol. 26, no. 11, pp. 1835–1842, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
3. F. Gu, “The new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings,” Journal of Mathematical Analysis and Applications, vol. 329, no. 2, pp. 766–776, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
4. M. O. Osilike, “Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps,” Journal of Mathematical Analysis and Applications, vol. 294, no. 1, pp. 73–81, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
5. Y. Su and S. Li, “Composite implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps,” Journal of Mathematical Analysis and Applications, vol. 320, no. 2, pp. 882–891, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
6. H.-K. Xu and R. G. Ori, “An implicit iteration process for nonexpansive mappings,” Numerical Functional Analysis and Optimization, vol. 22, no. 5-6, pp. 767–773, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
7. Y. Su, M. Li, and H. Zhang, “New monotone hybrid algorithm for hemi-relatively nonexpansive mappings and maximal monotone operators,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5458–5465, 2011. View at Publisher · View at Google Scholar
8. S. S. Chang, H. W. J. Lee, C. K. Chan, and J. K. Kim, “Approximating solutions of variational inequalities for asymptotically nonexpansive mappings,” Applied Mathematics and Computation, vol. 212, no. 1, pp. 51–59, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
9. H. Zegeye and N. Shahzad, “Convergence of Mann's type iteration method for generalized asymptotically nonexpansive mappings,” Computers & Mathematics with Applications, vol. 62, no. 11, pp. 4007–4014, 2011. View at Publisher · View at Google Scholar
10. 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
11. S. S. Chang, L. Wang, Y.-K. Tang, B. Wang, and L.-J. Qin, “Strong convergence theorems for a countable family of quasi-$\phi$-asymptotically nonexpansive nonself mappings,” Applied Mathematics and Computation, vol. 218, no. 15, pp. 7864–7870, 2012. View at Publisher · View at Google Scholar
12. W. Nilsrakoo, “Halpern-type iterations for strongly relatively nonexpansive mappings in Banach spaces,” Computers & Mathematics with Applications, vol. 62, no. 12, pp. 4656–4666, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
13. S. S. Chang, H. W. J. Lee, C. K. Chan, and J. ai Liu, “Strong convergence theorems for countable families of asymptotically relatively nonexpansive mappings with applications,” Applied Mathematics and Computation, vol. 218, no. 7, pp. 3187–3198, 2011. View at Publisher · View at Google Scholar
14. W. Nilsrakoo and S. Saejung, “Strong convergence theorems by Halpern-Mann iterations for relatively nonexpansive mappings in Banach spaces,” Applied Mathematics and Computation, vol. 217, no. 14, pp. 6577–6586, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
15. S. Suantai, W. Cholamjiak, and P. Cholamjiak, “An implicit iteration process for solving a fixed point problem of a finite family of multi-valued mappings in Banach spaces,” Applied Mathematics Letters, vol. 25, no. 11, pp. 1656–1660, 2012. View at Publisher · View at Google Scholar
16. S. S. Chang, K. K. Tan, H. W. J. Lee, and C. K. Chan, “On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 313, no. 1, pp. 273–283, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
17. S. S. Chang, H. W. J. Lee, C. K. Chan, and W. B. Zhang, “A modified halpern-type iteration algorithm for totally quasi-$\phi$-asymptotically nonexpansive mappings with applications,” Applied Mathematics and Computation, vol. 218, no. 11, pp. 6489–6497, 2012. View at Publisher · View at Google Scholar
18. X. Qin, S. Y. Cho, and S. M. Kang, “Strong convergence of shrinking projection methods for quasi-$\phi$-nonexpansive mappings and equilibrium problems,” Journal of Computational and Applied Mathematics, vol. 234, no. 3, pp. 750–760, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
19. D. Wu, S. S. Chang, and G. X. Yuan, “Approximation of common fixed points for a family of finite nonexpansive mappings in Banach space,” Nonlinear Analysis, vol. 63, no. 5-7, pp. 987–999, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
20. C. Zhang, J. Li, and B. Liu, “Strong convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces,” Computers & Mathematics with Applications, vol. 61, no. 2, pp. 262–276, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
21. M. O. Osilike, A. Udomene, D. I. Igbokwe, and B. G. Akuchu, “Demiclosedness principle and convergence theorems for $k$-strictly asymptotically pseudocontractive maps,” Journal of Mathematical Analysis and Applications, vol. 326, no. 2, pp. 1334–1345, 2007. View at Publisher · View at Google Scholar
22. K. Nakajo and W. Takahashi, “Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups,” Journal of Mathematical Analysis and Applications, vol. 279, no. 2, pp. 372–379, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
23. H.-K. Xu, “Strong convergence of approximating fixed point sequences for nonexpansive mappings,” Bulletin of the Australian Mathematical Society, vol. 74, no. 1, pp. 143–151, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
24. S.-Y. Matsushita and W. Takahashi, “Approximating fixed points of nonexpansive mappings in a Banach space by metric projections,” Applied Mathematics and Computation, vol. 196, no. 1, pp. 422–425, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
25. H. Dehghan, “Approximating fixed points of asymptotically nonexpansive mappings in Banach spaces by metric projections,” Applied Mathematics Letters, vol. 24, no. 9, pp. 1584–1587, 2011. View at Publisher · View at Google Scholar
26. S. M. Kang and S. Wang, “New hybrid algorithms for nonexpansive mappings in Banach spaces,” International Journal of Mathematical Analysis, vol. 5, no. 9-12, pp. 433–440, 2011.
27. 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, Dekker, New York, NY, USA, 1996. View at Zentralblatt MATH
28. W. Takahashi, Nonlinear Function Analysis. Fixed Points Theory and Its Applications, Yokohama Publishers, Yokohama, 2000.
29. F. E. Browder, “Convergence theorems for sequences of nonlinear operators in Banach spaces,” Mathematische Zeitschrift, vol. 100, pp. 201–225, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
30. D. Pascali and S. Sburlan, Nonlinear Mappings of Monotone Type, Noordhoff, Leyden, Mass, USA, 1978.
31. M. O. Osilike, S. C. Aniagbosor, and B. G. Akuchu, “Fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces,” Panamerican Mathematical Journal, vol. 12, no. 2, pp. 77–88, 2002. View at Zentralblatt MATH
32. H. K. Xu, “Inequalities in Banach spaces with applications,” Nonlinear Analysis, vol. 16, no. 12, pp. 1127–1138, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
33. R. E. Bruck, “On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces,” Israel Journal of Mathematics, vol. 38, no. 4, pp. 304–314, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH