Auxiliary principle and iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities

In this paper, we extend the auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequa lities. We prove the existence of a solution of the auxiliary problem for t he generalized set-valued strongly nonlinear mixed variational-like inequal ities, construct the iterative algorithm for the generalized set-valued str ongly nonlinear mixed variational-like inequalities, and show the existence of a solution of the generalized set-valued strongly nonlinear mixed varia tional-like inequality by using the auxiliary principle technique. We also prove the convergence of iterative sequences generated by the algorithm. (C ) 2001 Academic Press.