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Abstract and Applied Analysis
Volume 2015 (2015), Article ID 451320, 10 pages
http://dx.doi.org/10.1155/2015/451320
Research Article

Approximating Iterations for Nonexpansive and Maximal Monotone Operators

1School of Mathematics & Information Technology, Nanjing Xiaozhuang University, Nanjing 211171, China
2Department of Mathematics, Gyeongsang National University, Jinju 660-701, Republic of Korea
3Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
4School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan 750021, China

Received 29 May 2014; Accepted 3 August 2014

Academic Editor: Poom Kumam

Copyright © 2015 Zhangsong Yao 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

We present two algorithms for finding a zero of the sum of two monotone operators and a fixed point of a nonexpansive operator in Hilbert spaces. We show that these two algorithms converge strongly to the minimum norm common element of the zero of the sum of two monotone operators and the fixed point of a nonexpansive operator.