Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 543061, 17 pages
Research Article

Solvability Criteria for Some Set-Valued Inequality Systems

Department of Mathematics, College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210009, China

Received 23 May 2010; Accepted 9 July 2010

Academic Editor: Qamrul Hasan Ansari

Copyright © 2010 Yingfan Liu. 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.


Arising from studying some multivalued von Neumann model, three set-valued inequality systems are introduced, and two solvability questions are considered. By constructing some auxiliary functions and studying their minimax and saddle-point properties, solvability criteria composed of necessary and sufficient conditions regarding these inequality systems are obtained.