Hybrid extragradient‐like methods for generalized mixed equilibrium problems, systems of generalized equilibrium problems and optimization problems

In this paper, we introduce and analyze a new hybrid extragradient‐like iterative algorithm for finding a common solution of a generalized mixed equilibrium problem, a system of generalized equilibrium problems and a fixed point problem of infinitely many non expansive mappings. Under some mild conditions, we prove the strong convergence of the sequence generated by the proposed algorithm to a common solution of these three problems. Such solution also solves an optimization problem. Several special cases are also discussed. The results presented in this paper are the supplement, extension, improvement and generalization of the previously known results in this area.