International Journal of Mathematics and Mathematical Sciences 
Volume 2004 (2004), Issue 70, Pages 3849-3857
doi:10.1155/S0161171204404426

Convergence and stability of the three-step iterative schemes for a class of general quasivariational-like inequalities

Zeqing Liu,1 Zhefu An,2 Shin Min Kang,3 and Jeong Sheok Ume4

 1Department of Mathematics, Liaoning Normal University, P. O. Box 200, Dalian 116029, Liaoning, China
2Department of Mathematics, Liaoning University, Shenyang 110036, Liaoning, China
3Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Chinju 660-701, Korea
4Department of Applied Mathematics, Changwon National University, Changwon 641-773, Korea
Received 27 April 2004

Abstract

We introduce and study a class of general quasivariational-like inequalities in Hilbert spaces, suggest two general algorithms, and establish the existence and uniqueness of solutions for these kinds of inequalities. Under certain conditions, we discuss convergence and stability of the three-step iterative sequences generated by the algorithms.