Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces

作者：Agarwal Ravi P; Cho Yeol J E; Petrot Narin^*

来源：Fixed Point Theory and Applications, 2011.

DOI：10.1186/1687-1812-2011-31

• set-valued mixed variational inequalities
• maximal monotone operator
• resolvent operator
• strongly monotone operator
• Hausdorff metric

In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties, due to the presence of a proper convex lower semi-continuous function, phi and a mapping g, which appeared in the considered problem, we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued (mixed) variational inequalities problems, it is clear that it cannot be directly applied to the problems that we have considered in this paper because of phi and g.

• 出版日期2011