Split General Strong Nonlinear Quasi-Variational Inequality Problem

We introduce a split general strong nonlinear quasi-variational inequality problem which is a natural extension of a split general quasi-variational inequality problem, split variational inequality problem, and quasi-variational and variational inequality problems in Hilbert spaces. Using the projection method, we propose an iterative algorithm for the split general strongly nonlinear quasi-variational inequality problem and discuss the convergence criteria of the iterative algorithm. The results presented here generalized, unify, and improve many previously known results for quasi-variational and variational inequality problems