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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 912545, 11 pages
Strong Convergence Theorems for Modifying Halpern Iterations for Quasi--Asymptotically Nonexpansive Multivalued Mapping in Banach Spaces with Applications
School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China
Received 20 August 2012; Accepted 21 November 2012
Academic Editor: Nan-Jing Huang
Copyright © 2012 Li Yi. 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.
- 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.
- 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, A. G. Kartosator, Ed., vol. 178 of Lecture Notes in Pure and Applied Mathematics, pp. 15–50, Marcel Dekker, New York, NY, USA, 1996.
- S. S. Chang, C. K. Chan, and H. W. J. Lee, “Modified block iterative algorithm for quasi-ϕ-asymptotically nonexpansive mappings and equilibrium problem in Banach spaces,” Applied Mathematics and Computation, vol. 217, no. 18, pp. 7520–7530, 2011.
- W. R. Mann, “Mean value methods in iteration,” Proceedings of the American Mathematical Society, vol. 4, pp. 506–510, 1953.
- A. Genel and J. Lindenstrauss, “An example concerning fixed points,” Israel Journal of Mathematics, vol. 22, no. 1, pp. 81–86, 1975.
- B. Halpern, “Fixed points of nonexpansive maps,” Bulletin of the American Mathematical Society, vol. 73, pp. 957–961, 1967.
- 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.
- S. Y. 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.
- S. Matsushita and W. Takahashi, “An iterative algorithm for relatively nonexpansive mappings by hybrid method and applications,” in Proceedings of the 3rd International Conference on Nonlinear Analysis and Convex Analysis, pp. 305–313, 2004.
- S.-y. 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.
- X. Qin, Y. J. Cho, S. M. Kang, and H. Zhou, “Convergence of a modified Halpern-type iteration algorithm for quasi-ϕ-nonexpansive mappings,” Applied Mathematics Letters. An International Journal of Rapid Publication, vol. 22, no. 7, pp. 1051–1055, 2009.
- Z. Wang, Y. Su, D. Wang, and Y. Dong, “A modified Halpern-type iteration algorithm for a family of hemi-relatively nonexpansive mappings and systems of equilibrium problems in Banach spaces,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2364–2371, 2011.
- 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.