Inertial algorithm for approximating a common fixed point for a countable family of relatively nonexpansive maps

In this paper, we study an inertial algorithm for approximating a common fixed point for a countable family of relatively nonexpansive maps in a uniformly convex and uniformly smooth real Banach space. We prove a strong convergence theorem. This theorem is an improvement of the result of Matsushita and Takahashi (J. Approx. Theory 134:257–266, 2005 ) and the result of Dong et al. (Optim. Lett. 12:87–102, 2018 ). Finally, we give some applications of our theorem.