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Journal of Applied Mathematics
Volume 2014, Article ID 414031, 5 pages
Research Article

On an Iterative Method for Finding a Zero to the Sum of Two Maximal Monotone Operators

1School of Mathematical Science, Henan Institute of Science and Technology, Xinxiang 453003, China
2Department of Mathematics, Luoyang Normal University, Luoyang 471022, China

Received 2 March 2014; Revised 18 August 2014; Accepted 19 August 2014; Published 21 August 2014

Academic Editor: Luigi Muglia

Copyright © 2014 Hongwei Jiao and Fenghui Wang. 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.


In this paper we consider a problem that consists of finding a zero to the sum of two monotone operators. One method for solving such a problem is the forward-backward splitting method. We present some new conditions that guarantee the weak convergence of the forward-backward method. Applications of these results, including variational inequalities and gradient projection algorithms, are also considered.