Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem

In this paper, we 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, we show that one of the sequences converges strongly and the other converges weakly.

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Bibliographische Detailangaben
Veröffentlicht in:	Journal of optimization theory and applications 2007-06, Vol.133 (3), p.359-370
Hauptverfasser:	TADA, A, TAKAHASHI, W
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Convergence Equilibrium Exact sciences and technology Hilbert space Mapping Mathematical models Mathematical programming Operational research and scientific management Operational research. Management science Optimization Sequences Studies Theorems
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Beschreibung
Zusammenfassung:	In this paper, we 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, we show that one of the sequences converges strongly and the other converges weakly.
ISSN:	0022-3239 1573-2878
DOI:	10.1007/s10957-007-9187-z