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Strong convergence theorems for solutions of equilibrium problems and common fixed points of a finite family of asymptotically nonextensive nonself mappings. (English) Zbl 1473.47049

Summary: An iterative algorithm for finding a common element of the set of common fixed points of a finite family of asymptotically nonextensive nonself mappings and the set of solutions for equilibrium problems is discussed. A strong convergence theorem of common element is established in a uniformly smooth and uniformly convex Banach space.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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[1] Moudafi, A., Weak convergence theorems for nonexpansive mappings and equilibrium problems, Journal of Nonlinear and Convex Analysis, 9, 1, 37-43, (2008) · Zbl 1167.47049
[2] Tada, A.; Takahashi, W., Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem, Journal of Optimization Theory and Applications, 133, 3, 359-370, (2007) · Zbl 1147.47052
[3] Ceng, L.-C.; Yao, J.-C., A hybrid iterative scheme for mixed equilibrium problems and fixed point problems, Journal of Computational and Applied Mathematics, 214, 1, 186-201, (2008) · Zbl 1143.65049
[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, 1, 506-515, (2007) · Zbl 1122.47056
[5] Combettes, P. L.; Hirstoaga, S. A., Equilibrium programming in Hilbert spaces, Journal of Nonlinear and Convex Analysis, 6, 1, 117-136, (2005) · Zbl 1109.90079
[6] Alber, Y. I., Metric and generalized projection operators in Banach spaces: properties and applications, Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, 178, 15-50, (1996), New York, NY, USA: Marcel Dekker, New York, NY, USA · Zbl 0883.47083
[7] Chidume, C. E.; Khumalo, M.; Zegeye, H., Generalized projection and approximation of fixed points of nonself maps, Journal of Approximation Theory, 120, 2, 242-252, (2003) · Zbl 1022.47049
[8] Liu, Y., Convergence theorems for common fixed points of nonself asymptotically nonextensive mappings, Journal of Optimization Theory and Applications, (2013) · Zbl 1311.90174
[9] Yang, L.; Xie, X., Weak and strong convergence theorems of three step iteration process with errors for nonself-asymptotically nonexpansive mappings, Mathematical and Computer Modelling, 52, 5-6, 772-780, (2010) · Zbl 1202.65069
[10] Matsushita, S.-y.; Takahashi, W., A strong convergence theorem for relatively nonexpansive mappings in a Banach space, Journal of Approximation Theory, 134, 2, 257-266, (2005) · Zbl 1071.47063
[11] Xu, H. K., Inequalities in Banach spaces with applications, Nonlinear Analysis. Theory, Methods & Applications, 16, 12, 1127-1138, (1991) · Zbl 0757.46033
[12] Blum, E.; Oettli, W., From optimization and variational inequalities to equilibrium problems, The Mathematics Student, 63, 1–4, 123-145, (1994) · Zbl 0888.49007
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