Academic Editor: W. A. Kirk
Copyright © 2010 Somyot Plubtieng and Wanna Sriprad. 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 present two iterative schemes with errors which are proved to be strongly convergent
to a common element of the set of fixed points of a countable family of relatively nonexpansive mappings
and the set of fixed points of nonexpansive mappings in the sense of Lyapunov functional in a real uniformly
smooth and uniformly convex Banach space. Using the result we consider strong convergence theorems for
variational inequalities and equilibrium problems in a real Hilbert space and strong convergence theorems
for maximal monotone operators in a real uniformly smooth and uniformly convex Banach space.