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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 489629, 13 pages
Strong and Weak Convergence Theorems for Equilibrium Problems and Weak Relatively Uniformly Nonexpansive Multivalued Mappings in Banach Spaces
Department of Foundation, Shandong Yingcai University, Jinan 250104, China
Received 22 August 2012; Accepted 21 September 2012
Academic Editor: Yongfu Su
Copyright © 2012 Zi-Ming 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.
- Y. Su, “On the weak relatively nonexpansive multi-valued mappings in Banach spaces,” Abstract and Applied Analysis, vol. 2012, Article ID 730619, 7 pages, 2012.
- S. Homaeipour and A. Razani, “Weak and strong convergence theorems for relatively nonexpansive multi-valued mappings in Banach spaces,” Fixed Point Theory and Applications, vol. 2011, article 73, 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.
- 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.
- A. Moudafi, “Second-order differential proximal methods for equilibrium problems,” JIPAM, vol. 4, no. 1, article 18, 2003.
- N. Shahzad and H. Zegeye, “Strong convergence results for nonself multimaps in Banach spaces,” Proceedings of the American Mathematical Society, vol. 136, no. 2, pp. 539–548, 2008.
- N. Shahzad and H. Zegeye, “On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 3-4, pp. 838–844, 2009.
- Y. Song and H. Wang, “Convergence of iterative algorithms for multivalued mappings in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 4, pp. 1547–1556, 2009.
- J. S. Jung, “Strong convergence theorems for multivalued nonexpansive nonself-mappings in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 66, no. 11, pp. 2345–2354, 2007.
- 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, 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.
- 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.
- 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 Appl. Math., pp. 15–50, Dekker, New York, 1996.
- W. Takahashi, Nonlinear Functional Analysis, Yokohama, Yokohama, Japan, 2000.