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http://dx.doi.org/10.14317/jami.2011.29.5_6.1179

A NEW METHOD FOR A FINITE FAMILY OF PSEUDOCONTRACTIONS AND EQUILIBRIUM PROBLEMS  

Anh, P.N. (Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology)
Son, D.X. (Hanoi Institute of Mathematics)
Publication Information
Journal of applied mathematics & informatics / v.29, no.5_6, 2011 , pp. 1179-1191 More about this Journal
Abstract
In this paper, we introduce a new iterative scheme for finding a common element of the set of fixed points of a finite family of strict pseudocontractions and the solution set of pseudomonotone and Lipschitz-type continuous equilibrium problems. The scheme is based on the idea of extragradient methods and fixed point iteration methods. We show that the iterative sequences generated by this algorithm converge strongly to the common element in a real Hilbert space.
Keywords
Strict pseudocontractions; pseudomonotone; Lipschitz-type continuous; equilibrium problems; extragradient methods; fixed point;
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1 S. Wang, and B. Guo, New Iterative Scheme with Nonexpansive Mappings for Equilibrium Problems and Variational Inequality Problems in Hilbert Spaces, J. of Comp. and Appl. Math., 233 (2010), 2620-2630.   DOI   ScienceOn
2 Y. Yao, Y.C. Liou, and Y.J, Wu, An Extragradient Method for Mixed Equilibrium Problems and Fixed Point Problems, Fixed Point Theory and Appl., (2009), dot: 10.1155/2009/632819.
3 L.C. Zeng, and J.C. Yao, Strong Convergence Theorem by an Extragradient Method for Fixed Point Problems and Variational Inequality Problems, Taiwanese J. of Math., 10 (2010), 1293-1303.
4 J.W. Peng, Iterative Algorithms for Mixed Equilibrium Problems, Strict Pseudocontrac- tions and Monotone Mappings, J. of Opt. Theory and Appl., 144 (2010), 107-119.   DOI
5 S. Schaible, S. Karamardian, and J.P. Crouzeix, Characterizations of Generalized Monotone Maps, J. of Opt. Theory and Appl., 76 (1993), 399-413.   DOI   ScienceOn
6 R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
7 S. Takahashi, and W. Takahashi, Viscosity Approximation Methods for Equilibrium Prob- lems and Fixed Point Problems in Hilbert Spaces, J. of Math. Anal. and Appl., 331 (2007), 506-515.   DOI   ScienceOn
8 S. Takahashi, and M. Toyoda, Weakly Convergence Theorems for Nonexpansive Mappings and Monotone Mappings, J. of Opt. Theory and Appl., 118 (2003), 417-428.   DOI   ScienceOn
9 S. Wang, Y.J. Cho, and X. Qin, A New Iterative Method for Solving Equilibrium Problems and Fixed Point Problems for Infinite Family of Nonexpansive Mappings, Fixed Point Theory and Appl., (2010), doi: 10.1155/2010/165098.
10 L.C. Ceng, A. Petrusel, C. Lee, and M.M. Wong, Two Extragradient Approximation Meth- ods for Variational Inequalities and Fixed Point Problems of Strict Pseudocontractions, Taiwanese J. of Math., 13 (2009), 607-632.
11 R. Chen, X. Shen, and S. Cui, Weak and Strong Convergence Theorems for Equilibrium Problems and Countable Strict Pseudocontractions Mappings in Hilbert Space, J. of Ineq. and Appl., (2010), doi:10.1155/2010/474813.
12 P. Daniele, F. Giannessi, and A. Maugeri, Equilibrium Problems and Variational Models , Kluwer Academic Publisher, 2003.
13 K. Goebel, and W.A.Kirk, Topics on Metric Fixed Point Theory, Cambridge University Press, Cambridge, England, 1990.
14 G. Mastroeni, Gap Function for Equilibrium Problems, J. of Global Opt., 27 (2004), 411-426.
15 P.N. Anh, A hybrid extragradient method for pseudomonotone equilibrium problems and fixed point problems, Accepted by B. of the Malaysian Math. Sci. Soc., 2011.
16 C. Marino-Yanes, and H.K. Xu, Strong Convergence of the CQ Method for Fixed Point Processes, Nonl. Anal., 64 (2006), 2400-2411.   DOI   ScienceOn
17 N. Nadezhkina, and W. Takahashi, Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings, J. of Opt. Theory and Appl., 128 (2006), 191-201.   DOI   ScienceOn
18 G.L. Acedo, and H.K. Xu, Iterative Methods for Strict Sseudo-Contractions in Hilbert Spaces. Nonl. Anal., 67 (2007), 2258-2271.   DOI   ScienceOn
19 P.N. Anh, A Logarithmic Quadratic Regularization Method for Solving Pseudomonotone Equilibrium Problems, Acta Math. Vietnamica, 34 (2009), 183-200.
20 P.N. Anh, An LQP Regularization Method for Equilibrium Problems on Polyhedral, Vietnam J. of Math., 36 (2008), 209-228.
21 P.N. Anh, and J.K. Kim, The Interior Proximal Cutting Hyperplane Method for Multivalued Variational Inequalities, J. of Nonl. and Convex Anal., 11 (2010), 491-502.
22 P. N. Anh, J. K. Kim, D. T. Binh and D. H. Phuc, A Proximal Point-Type Algorithm for Solving NonLipschitzian Multivalued Variational Inequalities, Vietnam J. of Math., 38 (2010), 413-423.
23 E. Blum, and W. Oettli, From Optimization and Variational Inequality to Equilibrium Problems, The Math. Stud., 63 (1994), 127-149.