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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 698593, 8 pages
Research Article

Iterative Algorithms for New General Systems of Set-Valued Variational Inclusions Involving -Maximal Relaxed Monotone Operators

1Department of Mathematics, Sichuan University of Science & Engineering, Zigong, Sichuan 643000, China
2Artificial Intelligence Key Laboratory of Sichuan Province, Zigong, Sichuan 643000, China

Received 24 March 2014; Accepted 16 May 2014; Published 5 June 2014

Academic Editor: Jian-Wen Peng

Copyright © 2014 Ting-jian Xiong and Heng-you Lan. 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 and study a class of new general systems of set-valued variational inclusions involving -maximal relaxed monotone operators in Hilbert spaces. By using the general resolvent operator technique associated with -maximal relaxed monotone operators, we construct some new iterative algorithms for finding approximation solutions to the general system of set-valued variational inclusion problem and prove the convergence of this algorithm. Our results improve and extend some known results.