title: The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems.
abstract: 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.
authors.affiliation: Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod Bangkok, 10140 Thailand.
authors.forename: Siwaporn
authors.initials: S
authors.lastname: Saewan
authors.forename: Poom
authors.initials: P
authors.lastname: Kumam
keywords: 47H05; 47H09; 47H10; A system of equilibrium problem; Hybrid block iterative algorithm; Inverse-strongly monotone operator; Uniformly quasi- ϕ-asymptotically nonexpansive mapping; Variational inequality