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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 172061, 10 pages
http://dx.doi.org/10.1155/2012/172061
Research Article

The Tikhonov Regularization Method for Set-Valued Variational Inequalities

Department of Mathematics, Sichuan Normal University Chengdu, Sichuan 610066, China

Received 16 December 2011; Accepted 1 February 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Yiran He. 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

This paper aims to establish the Tikhonov regularization theory for set-valued variational inequalities. For this purpose, we firstly prove a very general existence result for set-valued variational inequalities, provided that the mapping involved has the so-called variational inequality property and satisfies a rather weak coercivity condition. The result on the Tikhonov regularization improves some known results proved for single-valued mapping.