Copyright © 2009 Gang Cai and Chang song Hu. 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 modifications of the Mann iteration, by using the hybrid methods,
for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings in a
Hilbert space. Then, we prove that such two sequences converge strongly to a common element of the set of
solutions of an equilibrium problem and the set of common fixed points of an infinite family of asymptotically
nonexpansive mappings. Our results improve and extend the results announced by many others.