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Hybrid iterative scheme for generalized equilibrium problems and fixed point problems of finite family of nonexpansive mappings. (English) Zbl 1226.47076
Summary: We introduce a new mapping and a hybrid iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a Hilbert space. Then we prove the strong convergence of the proposed iterative algorithm to a common fixed point of a finite family of nonexpansive mappings which is a solution of the generalized equilibrium problem. The results obtained in this paper extend the recent ones of S. Takahashi and W. Takahashi [Nonlinear Anal., Theory Methods Appl. 69, No. 3, A, 1025–1033 (2008; Zbl 1142.47350)].
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties