Communications of the
Korean Mathematical Society CKMS

In this paper, we introduce and study a new class of generalized mixed quasi-variational-like inequalities. Using the auxiliary principle technique, we construct a new iterative algorithm for finding the approximate solutions of the generalized mixed quasi-variational-like inequality. An existence result of solutions for the generalized mixed quasi-variational-like inequality and the convergence of the iterative algorithm are also established. Our results extend, unify and improve many recent known results.

Keywords: generalized mixed quasi-variational-like inequality, auxiliary pri\-nciple technique, iterative algorithm, convergence

MSC numbers: 47J20, 49J40