Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 798319, 20 pages
doi:10.1155/2009/798319

On strong convergence by the hybrid method for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings

Abstract

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.