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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 654537, 7 pages
http://dx.doi.org/10.1155/2013/654537
Research Article

A System of Generalized Variational Inclusions Involving a New Monotone Mapping in Banach Spaces

School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

Received 17 April 2013; Accepted 13 July 2013

Academic Editor: Micah Osilike

Copyright © 2013 Jinlin Guan and Changsong Hu. 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 introduce a new monotone mapping in Banach spaces, which is an extension of the -monotone mapping studied by Nazemi (2012), and we generalize the variational inclusion involving the -monotone mapping. Based on the new monotone mapping, we propose a new proximal mapping which combines the proximal mapping studied by Nazemi (2012) with the mapping studied by Lan et al. (2011) and show its Lipschitz continuity. Based on the new proximal mapping, we give an iterative algorithm. Furthermore, we prove the convergence of iterative sequences generated by the algorithm under some appropriate conditions. Our results improve and extend corresponding ones announced by many others.