Viscosity iteration method for variational inclusions, equilibria and fixed points on Hadamard manifolds

In this paper, we first introduce a viscosity iteration method for finding a common solution of a countable family of quasi-variational inclusion problems, an equilibrium problem (for short, EP) and a fixed-point problem of a nonexpansive mapping on Hadamard manifolds.Then, under some mild conditions, we prove that the iterative sequence generated by the suggested algorithm converges to a common solution.As applications, we utilize our main result to deal with the minimization problem with EP constraint and the variational inequality problem with EP constraint on Hadamard manifolds, respectively.