Strong convergence theorems for a countable family of quasi-ϕ-asymptotically nonexpansive nonself mappings

The purpose of this article is to introduce a class of quasi-ϕ-asymptotically nonexpansive nonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper improve and extend the corresponding results announced by some authors recently.