The Tikhonov Regularization Method for Set-Valued Variational Inequalities

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.