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An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings. (English) Zbl 1167.47307
Summary: We propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a strict pseudo-contraction mapping in the setting of real Hilbert spaces. We establish some weak and strong convergence theorems of the sequences generated by our proposed scheme. Our results combine the ideas of {\it G. Marino} and {\it H. K.\thinspace Xu} [J. Math. Anal. Appl. 329, No. 1, 336--346 (2007; Zbl 1116.47053)] and {\it S. Takahashi} and {\it W. Takahashi} [J. Math. Anal. Appl. 331, No. 1, 506--515 (2007; Zbl 1122.47056)]. In particular, necessary and sufficient conditions for the strong convergence of our iterative scheme are obtained.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47J20Inequalities involving nonlinear operators
65J15Equations with nonlinear operators (numerical methods)
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References:
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