Communications of the
Korean Mathematical Society CKMS

In this paper, we introduce and study a new class of the generalized set-valued mixed variational inequalities. Using the resolvent operator technique, we construct a new iterative algorithm for solving this class of the generalized set-valued mixed variational inequalities. We prove the existence of solutions for the generalized set-valued mixed variational inequalities and the convergence of the iterative sequences generated by the algorithm.

Keywords: generalized set-valued mixed variational inequality, resolvent operator, iterative algorithm

MSC numbers: 49J20, 49J40