Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 284363, 20 pages
Research Article

A General Iterative Approach to Variational Inequality Problems and Optimization Problems

Department of Mathematics, Dong-A University, Busan 604-714, Republic of Korea

Received 4 October 2010; Accepted 14 November 2010

Academic Editor: Jen Chih Yao

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.