Approximating solutions of the generalized modification of the system of equilibrium problems and fixed point problem of a nonexpansive mapping

The purpose of this research is to study the generalized modification of the system of equilibrium problems (GMSEP) and a lemma is established to show the property of this problem. Then, we prove a strong convergence theorem for finding a common element of the set of the solutions of the fixed points problem and the set of the solutions of the GMSEP under some suitable conditions, in which , where are coefficients in the main iteration. Moreover, we prove strong convergence theorems for finding solutions to the generalized equilibrium problem, the system of equilibrium problems, the variational inequality problem, the general system of variational inequality problems, and the minimization problem. Finally, we give two numerical examples, one of which shows the rate of convergence of the main iteration while the other shows the rate of convergence of the main iteration but the sum of coefficients equals 1.