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Zbl 1147.47052
Tada, A.; Takahashi, W.
Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem. (English)
[J] J. Optim. Theory Appl. 133, No. 3, 359-370 (2007). ISSN 0022-3239; ISSN 1573-2878/e

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.
[Jinhai Chen (Hongkong)]

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
49J40 Variational methods including variational inequalities
47H09 Mappings defined by "shrinking" properties
91B50 Equilibrium in economics

Keywords: equilibrium problems; nonexpansive mappings; firmly nonexpansive mappings; weak and strong convergence; monotonicity

Cited in: Zbl 1204.49006 Zbl 1191.65065 Zbl 1220.47102 Zbl 1189.49020 Zbl 1167.47050 Zbl 1162.47051

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