Journal of Inequalities and Applications
Volume 7 (2002), Issue 6, Pages 807-828
Generalized nonlinear mixed implicit quasi-variational inclusions with set-valued mappings
1Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore
2Department of Mathematics, Sichuan University, Sichuan, Chengdu 610064, China
3Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea
Received 10 January 2001; Revised 20 June 2001
Copyright © 2002 R. P. Agarwal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper, we introduce and study a new class of implicit quasi-variational inclusions, which is called the generalized nonlinear mixed implicit quasi-variational inclusion with setvalued mappings. Using the resolvent operator technique for maximal monotone mapping, we construct some new iterative algorithms for solving this class of generalized nonlinear mixed implicit quasi-variational inclusions with non-compact set-valued mappings. We prove the existence of solution for this kind of generalized nonlinear mixed implicit quasivariational inclusions with non-compact set-valued mappings and the convergence of iterative sequences generated by the algorithms. We also discuss the convergence and stability of perturbed iterative algorithm with errors for solving a class of generalized nonlinear mixed implicit quasi-variational inclusions with single-valued mappings.