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Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem. (English) Zbl 1147.47052

The authors introduce two iterative sequences for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem in a Hilbert space. Then they show that one of the sequences converges strongly and the other converges weakly.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
49J40 Variational inequalities
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
91B50 General equilibrium theory
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