New system of generalized nonlinear co-complementarity problems

In this paper, we introduce and study a new system of generalized nonlinear co-complementarity problems with set-valued mappings and construct an iterative algorithm for approximating the solutions of the system of generalized co-complementarity problems. We prove the existence of the solutions for the system of generalized co-complementarity problems with set-valued mappings without compactness and the convergence of iterative sequences generated by the algorithm in Hubert spaces. We also study a new perturbed iterative algorithm for approximating a system of generalized co-complementarity problems with single-valued mappings in Hubert spaces. © 2006 Korean Society for Computational & Applied Mathematici and Korean SIGCAM.