Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 282171, 18 pages
doi:10.1155/2011/282171
Research Article

Iterative Approaches to Find Zeros of Maximal Monotone Operators by Hybrid Approximate Proximal Point Methods

Lu Chuan Ceng,1 Yeong Cheng Liou,2 and Eskandar Naraghirad3

1Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan
3Department of Mathematics, Yasouj University, Yasouj 75914, Iran

Received 18 August 2010; Accepted 23 September 2010

Academic Editor: Jen Chih Yao

Copyright © 2011 Lu Chuan Ceng et al. 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.

Abstract

The purpose of this paper is to introduce and investigate two kinds of iterative algorithms for the problem of finding zeros of maximal monotone operators. Weak and strong convergence theorems are established in a real Hilbert space. As applications, we consider a problem of finding a minimizer of a convex function.