Generalized nonlinear mixed quasi-variational inequalities☆

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Abstract

In this paper, we introduce and study a new class of quasi-variational inequalities, which is called the generalized nonlinear set-valued mixed quasi-variational inequality. Using the resolvent operator technique for maximal monotone mapping, we construct some new iterative algorithms for solving this class of generalized nonlinear set-valued mixed quasi-variational inequalities. We prove the existence of solution for this kind of generalized nonlinear set-valued mixed quasivariational inequalities without compactness and the convergence of iterative sequences generated by the algorithms. We also discuss the convergence and stability of perturbed iterative algorithm for solving a class of generalized nonlinear mixed quasi-variational inequalities.

Keywords

Mixed quasi-variational inequality
Set-valued mapping
Iterative algorithm
Perturbed algorithm
Stability

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The first author was supported in part by '98 APEC Post-Doctor Fellowship (KOSEF) while he visited Gyeongsang National University, and the third and fourth authors wish to acknowledge the financial support of the Korea Research Foundation made in the program year of 1998, Project No. 1998-015-D00020.

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