- 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 543040, 14 pages
Some Results on Strictly Pseudocontractive Nonself-Mappings and Equilibrium Problems in Hilbert Spaces
1School of Mathematics Physics and Information Science, Zhejiang Ocean University,
Zhoushan 316004, China
2Department of Mathematics, Gyeongsang National University, Jinju 660-701, Republic of Korea
Received 12 September 2012; Accepted 6 October 2012
Academic Editor: Yonghong Yao
Copyright © 2012 Yan Hao and Sun Young Cho. 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.
- 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.
- S. Park, “Some equilibrium problems in generalized convex spaces,” Acta Mathematica Vietnamica, vol. 26, no. 3, pp. 349–364, 2001.
- Q. H. Ansari, S. Schaible, and J.-C. Yao, “The system of generalized vector equilibrium problems with applications,” Journal of Global Optimization, vol. 22, no. 1–4, pp. 3–16, 2002.
- X. Qin, S.-S. Chang, and Y. J. Cho, “Iterative methods for generalized equilibrium problems and fixed point problems with applications,” Nonlinear Analysis: Real World Applications., vol. 11, no. 4, pp. 2963–2972, 2010.
- L.-J. Lin, Z.-T. Yu, Q. H. Ansari, and L.-P. Lai, “Fixed point and maximal element theorems with applications to abstract economies and minimax inequalities,” Journal of Mathematical Analysis and Applications, vol. 284, no. 2, pp. 656–671, 2003.
- S. Y. Cho and S. M. Kang, “Approximation of common solutions of variational inequalities via strict pseudocontractions,” Acta Mathematica Scientia B, vol. 32, no. 4, pp. 1607–1618, 2012.
- S. Y. Cho and S. M. Kang, “Approximation of fixed points of pseudocontraction semigroups based on a viscosity iterative process,” Applied Mathematics Letters, vol. 24, no. 2, pp. 224–228, 2011.
- T. Kotzer, N. Cohen, and J. Shamir, “Image restoration by a novel method of parallel projection onto constraint sets,” Optimization Letters, vol. 20, pp. 1772–1774, 1995.
- C. Byrne, “A unified treatment of some iterative algorithms in signal processing and image reconstruction,” Inverse Problems, vol. 20, no. 1, pp. 103–120, 2004.
- A. N. Iusem and W. Sosa, “Iterative algorithms for equilibrium problems,” Optimization, vol. 52, no. 3, pp. 301–316, 2003.
- Y. Censor, T. Elfving, N. Kopf, and T. Bortfeld, “The multiple-sets split feasibility problem and its applications for inverse problems,” Inverse Problems, vol. 21, no. 6, pp. 2071–2084, 2005.
- Y. J. Cho and X. Qin, “Systems of generalized nonlinear variational inequalities and its projection methods,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 12, pp. 4443–4451, 2008.
- G. Lopez, V. Martin, and H.-K. Xu, “Perturbation techniques for nonexpansive mappings with applications,” Nonlinear Analysis: Real World Applications, vol. 10, no. 4, pp. 2369–2383, 2009.
- X. Qin and Y. Su, “Strong convergence theorems for relatively nonexpansive mappings in a Banach space,” Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 6, pp. 1958–1965, 2007.
- S. M. Kang, S. Y. Cho, and Z. Liu, “Convergence of iterative sequences for generalized equilibrium problems involving inverse-strongly monotone mappings,” Journal of Inequalities and Applications, vol. 2010, Article ID 827082, 16 pages, 2010.
- F. E. Browder and W. V. Petryshyn, “Construction of fixed points of nonlinear mappings in Hilbert space,” Journal of Mathematical Analysis and Applications, vol. 20, pp. 197–228, 1967.
- H. Zhou, “Convergence theorems of fixed points for -strict pseudo-contractions in Hilbert spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 2, pp. 456–462, 2008.
- 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.
- X. Qin, S. Y. Cho, and S. M. Kang, “Strong convergence of shrinking projection methods for quasi--nonexpansive mappings and equilibrium problems,” Journal of Computational and Applied Mathematics, vol. 234, no. 3, pp. 750–760, 2010.
- J. Ye and J. Huang, “Strong convergence theorems for fixed point problems and generalized equilibrium problems of three relatively quasi-nonexpansive mappings in Banach spaces,” Journal of Mathematical and Computational Science, vol. 1, no. 1, pp. 1–18, 2011.
- J. K. Kim, S. Y. Cho, and X. Qin, “Some results on generalized equilibrium problems involving strictly pseudocontractive mappings,” Acta Mathematica Scientia B, vol. 31, no. 5, pp. 2041–2057, 2011.
- A. Tada and W. Takahashi, “Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem,” Journal of Optimization Theory and Applications, vol. 133, no. 3, pp. 359–370, 2007.
- J. K. Kim, “Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi--nonexpansive mappings,” Fixed Point Theory and Applications, vol. 2011, article 10, 2011.
- X. Qin, S. Y. Cho, and S. M. Kang, “On hybrid projection methods for asymptotically quasi--nonexpansive mappings,” Applied Mathematics and Computation, vol. 215, no. 11, pp. 3874–3883, 2010.
- S. Yang and W. Li, “Iterative solutions of a system of equilibrium problems in Hilbert spaces,” Advances in Fixed Point Theory, vol. 1, pp. 15–26, 2011.
- A. Moudafi, “Weak convergence theorems for nonexpansive mappings and equilibrium problems,” Journal of Nonlinear and Convex Analysis, vol. 9, no. 1, pp. 37–43, 2008.
- Y. Haugazeau, Sur les inéquations variationnelles et la minimisation de fonctionnelles convexes [Thése], Université de Paris, Paris, France, 1968.
- C. Martinez-Yanes and H.-K. Xu, “Strong convergence of the CQ method for fixed point iteration processes,” Nonlinear Analysis: Theory, Methods & Applications, vol. 64, no. 11, pp. 2400–2411, 2006.
- W. Takahashi, Y. Takeuchi, and R. Kubota, “Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 341, no. 1, pp. 276–286, 2008.