Iterative method for a finite family of nonexpansive mappings in Hilbert spaces with applications

In this paper, we introduce a new iterative method for finding a commonelement of the set of solutions of a general system of variationalinequalities, the set of solutions of a mixed equilibrium problem and theset of common fixed points of a finite family of nonexpansive mappingsin a real Hilbert space. Furthermore, we prove that the studied iterativemethod converges strongly to a common element of these three sets.Consequently, we apply our main result to the problem of approximatinga zero of a finite family of maximal monotone mappings in Hilbertspaces. The theorems presented in this paper, improve and extend thecorresponding results of Takahashi and Toyoda [18] and many others.