Hemivariational-like inequalities

In this paper, we introduce and consider a new class of variational inequalities, known as the hemivariational-like inequalities. It is shown that the hemivariational-like inequalities include hernivariational inequalities, variational-like inequalities and the classical variational inequalities as special cases. The auxiliary principle is used to suggest C, and analyze some iterative methods for solving hemivariational-like inequalities under mild conditions. The results obtained in this paper can be considered as a novel application of the auxiliary principle technique. (c) 2004 Elsevier B.V. All rights reserved.