- 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 2012 (2012), Article ID 818970, 14 pages
Modified Relaxed Extragradient Method for a General System of Variational Inequalities and Nonexpansive Mappings in Banach Spaces
Department of Mathematics, Zhejiang Normal University, Zhejiang 321004, China
Received 15 May 2012; Accepted 8 June 2012
Academic Editor: Yonghong Yao
Copyright © 2012 Yuanheng Wang and Liu Yang. 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.
- G. Stampacchia, “Formes bilinéaires coercitives sur les ensembles convexes,” Comptes Rendus de l'Académie des Sciences, vol. 258, pp. 4413–4416, 1964.
- M. A. Noor, “Some algorithms for general monotone mixed variational inequalities,” Mathematical and Computer Modelling, vol. 29, no. 7, pp. 1–9, 1999.
- Y. Yao and M. A. Noor, “On viscosity iterative methods for variational inequalities,” Journal of Mathematical Analysis and Applications, vol. 325, no. 2, pp. 776–787, 2007.
- M. A. Noor, “New approximation schemes for general variational inequalities,” Journal of Mathematical Analysis and Applications, vol. 251, no. 1, pp. 217–229, 2000.
- M. Aslam Noor, “Some developments in general variational inequalities,” Applied Mathematics and Computation, vol. 152, no. 1, pp. 199–277, 2004.
- R. U. Verma, “Generalized system for relaxed cocoercive variational inequalities and projection methods,” Journal of Optimization Theory and Applications, vol. 121, no. 1, pp. 203–210, 2004.
- S. S. Chang, H. W. Joseph Lee, and C. K. Chan, “Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces,” Applied Mathematics Letters, vol. 20, no. 3, pp. 329–334, 2007.
- L.-C. Ceng and J.-C. Yao, “An extragradient-like approximation method for variational inequality problems and fixed point problems,” Applied Mathematics and Computation, vol. 190, no. 1, pp. 205–215, 2007.
- X. Qin, S. M. Kang, and M. Shang, “Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces,” Applicable Analysis, vol. 87, no. 4, pp. 421–430, 2008.
- H. Iiduka and W. Takahashi, “Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings,” Nonlinear Analysis. Theory, Methods & Applications, vol. 61, no. 3, pp. 341–350, 2005.
- X. Qin, S. Y. Cho, and S. M. Kang, “Convergence of an iterative algorithm for systems of variational inequalities and nonexpansive mappings with applications,” Journal of Computational and Applied Mathematics, vol. 233, no. 2, pp. 231–240, 2009.
- L.-C. Ceng, C.-y. Wang, and J.-C. Yao, “Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities,” Mathematical Methods of Operations Research, vol. 67, no. 3, pp. 375–390, 2008.
- D. L. Zhu and P. Marcotte, “Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities,” SIAM Journal on Optimization, vol. 6, no. 3, pp. 714–726, 1996.
- Y. Yao, M. Aslam Noor, K. Inayat Noor, Y.-C. Liou, and H. Yaqoob, “Modified extragradient methods for a system of variational inequalities in Banach spaces,” Acta Applicandae Mathematicae, vol. 110, no. 3, pp. 1211–1224, 2010.
- 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.
- H. K. Xu, “Inequalities in Banach spaces with applications,” Nonlinear Analysis. Theory, Methods & Applications, vol. 16, no. 12, pp. 1127–1138, 1991.
- R. E. Bruck, Jr., “Nonexpansive retracts of Banach spaces,” Bulletin of the American Mathematical Society, vol. 76, pp. 384–386, 1970.
- T. Suzuki, “Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals,” Journal of Mathematical Analysis and Applications, vol. 305, no. 1, pp. 227–239, 2005.
- R. E. Bruck, Jr., “Properties of fixed-point sets of nonexpansive mappings in Banach spaces,” Transactions of the American Mathematical Society, vol. 179, pp. 251–262, 1973.
- S. Reich, “Asymptotic behavior of contractions in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 44, pp. 57–70, 1973.