Journal of Inequalities and Applications
Volume 5 (2000), Issue 4, Pages 381-395
Perturbed iterative algorithms with errors for completely generalized strongly nonlinear implicit quasivariational inclusions
1Department of Mathematics, Gyeongsang National University, Chinju 660-701, South Korea
2Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
Received 4 May 1999; Revised 27 July 1999
Copyright © 2000 S. H. Shim 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 a new class of completely generalized strongly nonlinear implicit
quasivariational inclusions and prove its equivalence with a class of fixed point problems by using some properties of maximal monotone mappings. We also prove the existence of solutions for the completely generalized strongly nonlinear implicit quasivariational inclusions and the convergence of iterative sequences generated by the perturbed algorithms with errors.