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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 {\it L.-C.\thinspace Ceng, C.-Y.\thinspace Wang} and {\it J.-C.\thinspace Yao} [Math. Methods Oper. Res. 67, No. 3, 375--390 (2008; Zbl 1147.49007)] and many others.

47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
Full Text: DOI
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