- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 573583, 6 pages
A New Iterative Method for Solving a System of Generalized Mixed Equilibrium Problems for a Countable Family of Generalized Quasi-ϕ-Asymptotically Nonexpansive Mappings
College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China
Received 3 October 2012; Accepted 4 January 2013
Academic Editor: Satit Saejung
Copyright © 2013 Wei-Qi Deng. 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.
- B. Ali and M. S. Minjibir, “Convergence of a hybrid iterative method for finite families of generalized quasi-ϕ-asymptotically nonexpansive mappings,” Fixed Point Theory and Applications, vol. 2012, article 121, 2012.
- 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.
- 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.
- S. Plubtieng and K. Ungchittrakool, “Hybrid iterative methods for convex feasibility problems and fixed point problems of relatively nonexpansive mappings in Banach spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 583082, 19 pages, 2008.
- S. S. Chang, H. W. Joseph Lee, and C. K. Chan, “A block hybrid method for solving generalized equilibrium problems and convex feasibility problem,” Advances in Computational Mathematics. In press.
- L.-C. Ceng, S.-M. Guu, H.-Y. Hu, and J.-C. Yao, “Hybrid shrinking projection method for a generalized equilibrium problem, a maximal monotone operator and a countable family of relatively nonexpansive mappings,” Computers & Mathematics with Applications, vol. 61, no. 9, pp. 2468–2479, 2011.
- Y. F. Su, H. K. Xu, and X. Zhang, “Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications,” Nonlinear Analysis. Theory, Methods & Applications, vol. 73, no. 12, pp. 3890–3906, 2010.
- E. U. Ofoedu and D. M. Malonza, “Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type,” Applied Mathematics and Computation, vol. 217, no. 13, pp. 6019–6030, 2011.
- 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.
- 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.
- Y. Yao, Y.-C. Liou, and S. M. Kang, “Strong convergence of an iterative algorithm on an infinite countable family of nonexpansive mappings,” Applied Mathematics and Computation, vol. 208, no. 1, pp. 211–218, 2009.
- H. Zegeye, E. U. Ofoedu, and N. Shahzad, “Convergence theorems for equilibrium problem, variational inequality problem and countably infinite relatively quasi-nonexpansive mappings,” Applied Mathematics and Computation, vol. 216, no. 12, pp. 3439–3449, 2010.
- 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.
- 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.
- S.-S. Zhang, “Generalized mixed equilibrium problem in Banach spaces,” Applied Mathematics and Mechanics, vol. 30, no. 9, pp. 1105–1112, 2009.
- S. S. Chang, J. K. Kim, and X. R. Wang, “Modified block iterative algorithm for solving convex feasibility problems in Banach spaces,” Journal of Inequalities and Applications, vol. 2010, Article ID 869684, 14 pages, 2010.
- 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.
- I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, vol. 62 of Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht, The Netherlands, 1990.
- S. S. Chang, H. W. J. Lee, C. K. Chan, and W. B. Zhang, “A modified halpern-type iteration algorithm for totally quasi-ϕ-asymptotically nonexpansive mappings with applications,” Applied Mathematics and Computation, vol. 218, no. 11, pp. 6489–6497, 2012.
- H. K. Xu, “Inequalities in Banach spaces with applications,” Nonlinear Analysis. Theory, Methods & Applications, vol. 16, no. 12, pp. 1127–1138, 1991.