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.
Reviewer: Jinhai Chen (Hongkong)
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 |
Keywords:
equilibrium problems; nonexpansive mappings; firmly nonexpansive mappings; weak and strong convergence; monotonicityReferences:
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