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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 651304, 11 pages
Strong Convergence Theorems for Asymptotically Weak -Pseudo--Contractive Non-Self-Mappings with the Generalized Projection in Banach Spaces
Department of Mathematics, Zhejiang Normal University, Zhejiang 321004, China
Received 28 August 2012; Revised 7 October 2012; Accepted 9 October 2012
Academic Editor: Xiaolong Qin
Copyright © 2012 Yuanheng 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.
- 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.
- J. Schu, “Iterative construction of fixed points of asymptotically nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 158, no. 2, pp. 407–413, 1991.
- X. Qin, Y. Su, and M. Shang, “Strong convergence for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappings,” Journal of the Korean Mathematical Society, vol. 45, no. 1, pp. 29–40, 2008.
- B. E. Rhoades, “Convergence of an Ishikawa-type iteration scheme for a generalized contraction,” Journal of Mathematical Analysis and Applications, vol. 185, no. 2, pp. 350–355, 1994.
- K.-K. Tan and H. K. Xu, “Fixed point iteration processes for asymptotically nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 122, no. 3, pp. 733–739, 1994.
- S. S. Chang, “Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 129, no. 3, pp. 845–853, 2001.
- X. Qin, T. Wang, and S. Y. Cho, “Hybrid projection algorithms for asymptotically strict quasi--pseudocontractions,” Abstract and Applied Analysis, vol. 2011, Article ID 142626, 13 pages, 2011.
- 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.
- C. E. Chidune, J. L. Li, and A. Vdomene, “Convergence of paths and approximation of fixed point of asymptotically non-expansive mapping,” Proceedings of the American Mathematical Society, vol. 133, no. 2, pp. 473–480, 2004.
- J. Li, “The metric projection and its applications to solving variational inequalities in Banach spaces,” Fixed Point Theory, vol. 5, no. 2, pp. 285–298, 2004.
- J. Li, “The generalized projection operator on reflexive Banach spaces and its applications,” Journal of Mathematical Analysis and Applications, vol. 306, no. 1, pp. 55–71, 2005.
- Y. Yao, M. A. Noor, and Y.-C. Liou, “Strong convergence of a modified extragradient method to the minimum-norm solution of variational inequalities,” Abstract and Applied Analysis, vol. 2012, Article ID 817436, 9 pages, 2012.
- Y.-C. Liou, Y. Yao, C.-W. Tseng, H.-T. Lin, and P.-X. Yang, “Iterative algorithms approach to variational inequalities and fixed point problems,” Abstract and Applied Analysis, vol. 2012, Article ID 949141, 15 pages, 2012.
- Y. Wang and L. Yang, “Modified relaxed extragradient method for a general system of variational in-equalities and nonexpansive mappings in Banach spaces,” Abstract and Applied Analysis, vol. 2012, Article ID 818970, 14 pages, 2012.
- Y. Alber and S. Guerre-Delabriere, “Principle of weakly contractive maps in Hilbert spaces,” Operator Theory, Advances and Applications, vol. 98, pp. 7–22, 1997.
- W. Xu and Y. Wang, “Strong convergence of the iterative methods for hierarchical fixed point problems of an infinite family of strictly nonself pseudocontractions,” Abstract and Applied Analysis, vol. 2012, Article ID 457024, 11 pages, 2012.