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Abstract and Applied Analysis
Volume 2013, Article ID 487545, 6 pages
Research Article

Multivalued Variational Inequalities with -Pseudomonotone Mappings in Reflexive Banach Spaces

1Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
2Department of Mathematics, University College, Umm Al-Qura University, Saudi Arabia

Received 28 August 2012; Accepted 31 January 2013

Academic Editor: Feyzi Başar

Copyright © 2013 A. M. Saddeek and S. A. Ahmed. 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.


This paper is concerned with the study of a class of variational inequalities with multivalued -pseudomonotone mappings in reflexive Banach spaces by using the -antiresolvent technique. An application to the multivalued nonlinear -complementarity problem is also presented. The results coincide with the corresponding results announced by many others for the gradient state.