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On iterative methods for equilibrium problems. (English) Zbl 1165.49035
Summary: We introduce a hybrid iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of finitely many nonexpansive mappings. We prove that the approximate solution converges strongly to a solution of a class of variational inequalities under some mild conditions, which is the optimality condition for some minimization problem. We also give some comments on the results of S. Plubtieng and R. Punpaeng [J. Math. Anal. Appl. 336, No. 1, 455–469 (2007; Zbl 1127.47053)]. Results obtained in this paper may be viewed as an improvement and refinement of the previously known results in this area.

MSC:
49M37 Numerical methods based on nonlinear programming
47H10 Fixed-point theorems
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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