## Weak and strong convergence theorems for equilibrium problems and countable strict pseudocontractions mappings in Hilbert space.(English)Zbl 1187.47046

Summary: We introduce two iterative sequences for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of strict pseudocontractions in Hilbert space. Then we study the weak and strong convergence of the sequences.

### MSC:

 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.

### Keywords:

strict pseudocontractions; Hilbert space; weak convergence
Full Text:

### References:

 [1] Blum, E; Oettli, W, From optimization and variational inequalities to equilibrium problems, The Mathematics Student, 63, 123-145, (1994) · Zbl 0888.49007 [2] Flam, SD; Antipin, AS, Equilibrium programming using proximal-like algorithms, Mathematical Programming, 78, 29-41, (1997) · Zbl 0890.90150 [3] Moudafi, A; Thera, M, Proximal and dynamical approaches to equilibrium problems, No. 477, 187-201, (1999), New York, NY, USA · Zbl 0944.65080 [4] Takahashi, S; Takahashi, W, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, Journal of Mathematical Analysis and Applications, 331, 506-515, (2007) · Zbl 1122.47056 [5] Aoyama, K; Kimura, Y; Takahashi, W; Toyoda, M, Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space, Nonlinear Analysis: Theory, Methods & Applications, 67, 2350-2360, (2007) · Zbl 1130.47045 [6] Marino, G; Xu, H-K, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, Journal of Mathematical Analysis and Applications, 329, 336-346, (2007) · Zbl 1116.47053 [7] Kim, T-H; Xu, H-K, Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis: Theory, Methods & Applications, 64, 1140-1152, (2006) · Zbl 1090.47059 [8] Martinez-Yanes, C; Xu, H-K, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Analysis: Theory, Methods & Applications, 64, 2400-2411, (2006) · Zbl 1105.47060 [9] Tada, A; Takahashi, W, Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem, Journal of Optimization Theory and Applications, 133, 359-370, (2007) · Zbl 1147.47052
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