Abstract
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.
Highlights
Variational inequalities are a very powerful tool of the current mathematical technology and have become a rich source of inspiration for scientists and engineers
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
We propose an iterative algorithm for the split general strongly nonlinear quasivariational inequality problem and discuss the convergence criteria of the iterative algorithm
Summary
Variational inequalities are a very powerful tool of the current mathematical technology and have become a rich source of inspiration for scientists and engineers. We propose an iterative algorithm for the split general strongly nonlinear quasivariational inequality problem and discuss the convergence criteria of the iterative algorithm. Kazmi [2] introduced and studied the following split general quasi-variational inequality problem (in short, SpGQVIP).
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