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http://dx.doi.org/10.7858/eamj.2013.021

CONVERGENCE THEOREMS FOR GENERALIZED EQUILIBRIUM PROBLEMS AND ASYMPTOTICALLY κ-STRICT PSEUDO-CONTRACTIONS IN HILBERT SPACES  

Liu, Ying (College of Mathematics and Computer, Hebei University)
Publication Information
East Asian mathematical journal / v.29, no.3, 2013 , pp. 303-314 More about this Journal
Abstract
In this paper, we introduce an iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem and the set of common fixed points of a finite family of asymptotically ${\kappa}$-strict pseudo-contractions in Hilbert spaces. Weak and strong convergence theorems are established for the iterative scheme.
Keywords
Metric projection; semi-compactness; Generalized equilibrium problem; Asymptotically ${\kappa}$-strict pseudo-contraction; Uniformly L-Lipschitzian;
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1 S. Takahashi, and W. Takahashi, Strong convergence theorems for a generalized equi-librium problem and a nonexpansive mapping in a Hilbert space, Nonlinear Anal. 69(2008), 1025-1033.   DOI   ScienceOn
2 S. Takahashi, and W. Takahashi, Viscosity approximation methods for equilibrium prob-lems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007), 506-515.   DOI   ScienceOn
3 W. Takahashi, and M. Toyoda, Weak convergence theorems for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl. 118 (2003), 417-428.   DOI   ScienceOn
4 K.K. Tan, and H.K. Xu, Approximating fixed points of nonexpansive mapping by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993), 301-308.   DOI   ScienceOn
5 E. Blum, and W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Stud. 63 (1994),123-145.
6 J. Chen, L. Zhang, and T. Fan, Viscosity approximation methods for nonexpansive mappings and monotone mappings, J. Math. Anal. Appl. 334 (2007), 1450-1461.   DOI   ScienceOn
7 P.L. Combettes,and A. Hirstoaga, Equilibrium programming in Hilbert spaces,J. Non-linear Convex Anal. 6 (2005), 117-136.
8 K. Goebel, and W.A. Kirk, A fixed point theorem for asymptotically nonexpansive map-pings, Proc. Amer. Math. Soc. 35 (1972), 171-174.   DOI   ScienceOn
9 H. Iiduka, and W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005), 341-350.   DOI   ScienceOn
10 T.H. Kim, and H.K. Xu, Convergence of the modified Manns iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal.68 (2008),2828-2836.   DOI   ScienceOn
11 L. Qihou, Convergence theorems of the sequence of iterates for asymptotically demicon- tractive and hemicontractive mappings, Nonlinear Anal. 26 (1996), 1835-1842.   DOI   ScienceOn
12 X. Qin, Y. Cho, S.Kang, and M. Shang, A hybrid iterative scheme for asymptotically k-strict pseudo-contractions in Hilbert spaces, Nonlinear Anal.70(2009),1902-1911.   DOI   ScienceOn
13 A. Tada, and W. Takahashi, Strong convergence theorem for an equilibrium problem and a nonexpansive mapping, J. Optim. Theory Appl. 133 (2007),359-370.   DOI