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A viscosity approximation method for equilibrium problems, fixed point problems of nonexpansive mappings and a general system of variational inequalities. (English) Zbl 1203.47064
Summary: We introduce and study a new iterative scheme for finding the common element of the set of common fixed points of a sequence of nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of the general system of variational inequality for $\alpha$ and $\mu$-inverse-strongly monotone mappings. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. This main theorem extends a recent result of L.-C. Ceng, C.-Y. Wang and J.-C. Yao [Math. Methods Oper. Res. 67, No. 3, 375–390 (2008; Zbl 1147.49007)] and many others.

##### MSC:
 47J25 Iterative procedures (nonlinear operator equations) 47H09 Mappings defined by “shrinking” properties 90C33 Complementarity and equilibrium problems; variational inequalities (finite dimensions)
##### References:
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