Copyright © 2011 Jong Soo Jung. 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 a new general iterative scheme for finding a common element of the set of
solutions of variational inequality problem for an inverse-strongly monotone mapping and the set of fixed
points of a nonexpansive mapping in a Hilbert space and then establish strong convergence of the sequence
generated by the proposed iterative scheme to a common element of the above two sets under suitable
control conditions, which is a solution of a certain optimization problem. Applications of the main result
are also given.