Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces
1 Department of Mathematical Sciences, Florida Institute Of Technology, 150 University BLD, Melbourne, FL 32901, USA
2 Department of Mathematics Education and the Rins Gyeongsang National University Chinju 660-701, Korea
3 Department of Mathematics Faculty Of Science, Naresuan University Phitsanulok 65000, Thailand
4 Centre of Excellence In Mathematics, Che, Si Ayutthaya Road, Bangkok 10400, Thailand
Fixed Point Theory and Applications 2011, 2011:31 doi:10.1186/1687-1812-2011-31Published: 11 August 2011
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, φ 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 φ and g.
2000 AMS Subject Classification: 47H05; 47H09; 47J25; 65J15.