## 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 G. Marino and H. K. Xu [J. Math. Anal. Appl. 329, No. 1, 336–346 (2007; Zbl 1116.47053)] and S. Takahashi and 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:

 47J25 Iterative procedures involving nonlinear operators 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems 47J20 Variational and other types of inequalities involving nonlinear operators (general) 65J15 Numerical solutions to equations with nonlinear operators

### Citations:

Zbl 1116.47053; Zbl 1122.47056
Full Text:

### References:

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