The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems - Saewan, Siwaporn; Kumam, Poom (SpringerPlus, 2012)
In this paper, we construct the hybrid block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi - ϕ - asymptotically nonexpansive mappings, the set of the solutions of the variational inequality for an α -inverse-strongly monotone operator, and the set of solutions of a system of equilibrium problems. Moreover, we obtain a strong convergence theorem for the sequence generated by this process in the framework Banach spaces. The results presented in this paper improve and generalize some well-known results in the literature.