Abstract
In this paper, we introduce composite extragradient iterative algorithms for finding a common element of the set of solutions of a general mixed equilibrium problem, the set of solutions of general system of variational inequalities, the set of solutions of finitely many variational inclusions, and the set of common fixed points of finitely many nonexpansive mappings and infinitely many strict pseudocontractions in a real Hilbert space. We derive the strong convergence of the proposed algorithms to a common element of these sets, which also solves some hierarchical minimization. The result presented in this paper improves and extends some corresponding ones in the earlier and recent literature.