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http://dx.doi.org/10.4134/JKMS.2009.46.3.561

WEAK AND STRONG CONVERGENCE THEOREMS FOR AN ASYMPTOTICALLY k-STRICT PSEUDO-CONTRACTION AND A MIXED EQUILIBRIUM PROBLEM  

Yao, Yong-Hong (DEPARTMENT OF MATHEMATICS TIANJIN POLYTECHNIC UNIVERSITY)
Zhou, Haiyun (DEPARTMENT OF MATHEMATICS SHIJIAZHUANG MECHANICAL ENGINEERING COLLEGE)
Liou, Yeong-Cheng (DEPARTMENT OF INFORMATION MANAGEMENT CHENG SHIU UNIVERSIT)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.3, 2009 , pp. 561-576 More about this Journal
Abstract
We introduce two iterative algorithms for finding a common element of the set of fixed points of an asymptotically k-strict pseudo-contraction and the set of solutions of a mixed equilibrium problem in a Hilbert space. We obtain some weak and strong convergence theorems by using the proposed iterative algorithms. Our results extend and improve the corresponding results of Tada and Takahashi [16] and Kim and Xu [8, 9].
Keywords
mixed equilibrium problems; fixed point problems; iterative algorithm; asymptotically k-strict pseudo-contraction; Hilbert space;
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1 E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student 63 (1994), no. 1-4, 123–145
2 O. Chadli, I. V. Konnov, and J. C. Yao, Descent methods for equilibrium problems in a Banach space, Comput. Math. Appl. 48 (2004), no. 3-4, 609–616
3 O. Chadli, S. Schaible, and J. C. Yao, Regularized equilibrium problems with application to noncoercive hemivariational inequalities, J. Optim. Theory Appl. 121 (2004), no. 3, 571–596   DOI   ScienceOn
4 M. A. Noor, Fundamentals of equilibrium problems, Math. Inequal. Appl. 9 (2006), no. 3, 529–566
5 S. Plubtieng and R. Punpaeng , A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 336 (2007), no. 1, 455–469   DOI   ScienceOn
6 A. Tada and W. Takahashi, Strong convergence theorem for an equilibrium problem and a nonexpansive mapping, Nonlinear analysis and convex analysis, 609–617, Yokohama Publ., Yokohama, 2007
7 A. Tada and W. Takahashi, Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem, J. Optim. Theory Appl. 133 (2007), no. 3, 359–370   DOI
8 S. D. Flam and A. S. Antipin, Equilibrium programming using proximal-like algorithms, Math. Programming 78 (1997), no. 1, Ser. A, 29–41   DOI
9 O. Chadli, N. C. Wong, and J. C. Yao, Equilibrium problems with applications to eigenvalue problems, J. Optim. Theory Appl. 117 (2003), no. 2, 245–266   DOI   ScienceOn
10 P. L. Combettes and S. A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal. 6 (2005), no. 1, 117–136
11 T. H. Kim and H. K. Xu, Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006), no. 5, 1140–1152   DOI   ScienceOn
12 I. V. Konnov, S. Schaible, and J. C. Yao, Combined relaxation method for mixed equilibrium problems, J. Optim. Theory Appl. 126 (2005), no. 2, 309–322   DOI
13 C. Matinez-Yanes and H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006), no. 11, 2400–2411   DOI   ScienceOn
14 L. C. Zeng, S. Y. Wu, and J. C. Yao, Generalized KKM theorem with applications to generalized minimax inequalities and generalized equilibrium problems, Taiwanese J. Math. 10 (2006), no. 6, 1497–1514
15 S. Takahashi and W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007), no. 1, 506–515   DOI   ScienceOn
16 Y. Yao, Y. C. Liou, and J. C. Yao, A new hybrid iterative algorithm for fixed point problems, variational inequality problems and mixed equilibrium problems, Fixed Point Theory and Applications 2008 (2008), Article ID 417089, 15 pages   DOI
17 Y. Yao, M. A. Noor, and Y. C. Liou, On iterative methods for equilibrium problems, Nonlinear Anal. 70 (2009), no. 1, 497–509   DOI   ScienceOn
18 T. H. Kim and H. K. Xu, Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions, Nonlinear Analysis: Theory, Methods & Applications 68 (2008), no. 9, 2828–2836   DOI   ScienceOn
19 Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591–597
20 X. P. Ding, Y. C. Lin, and J. C. Yao, Predictor-corrector algorithms for solving generalized mixed implicit quasi-equilibrium problems, Appl. Math. Mech. (English Ed.) 27 (2006), no. 9, 1157–1164   DOI   ScienceOn
21 Y. Yao, Y. C. Liou, and J. C. Yao, Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings, Fixed Point Theory Appl. 2007, Art. ID 64363, 12 pp   DOI   ScienceOn
22 L. C. Zeng and J. C. Yao, A hybrid iterative scheme for mixed equilibrium problems and fixed point problems , J. Comput. Appl. Math. 214 (2008), no. 1, 186–201   DOI   ScienceOn