Copyright © 2010 Daruni Boonchari and Satit Saejung. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We introduce two general iterative schemes for finding a common fixed point of a countable family of relatively nonexpansive mappings in a Banach space. Under suitable setting, we not only obtain several convergence theorems announced by many authors but also prove them under weaker assumptions. Applications to the problem of finding a common element of the fixed point set of a relatively nonexpansive mapping and the solution set of an equilibrium problem are also discussed.