, Volume 46, Issue 3, pp 447-464

A viscosity approximation method for equilibrium problems, fixed point problems of nonexpansive mappings and a general system of variational inequalities

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In this paper, 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 α and μ-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 Ceng et al. (Math Meth Oper Res 67:375–390, 2008) and many others.