Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 29863, 12 pages
Perturbed Iterative Algorithms for Generalized Nonlinear Set-Valued Quasivariational Inclusions Involving Generalized -Accretive Mappings
Department of Mathematics, Yangtze Normal University, Chongqing 408003, Fuling, China
Received 24 August 2006; Revised 10 January 2007; Accepted 14 January 2007
Academic Editor: H. Bevan Thompson
Copyright © 2007 Mao-Ming Jin. 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.
A new class of generalized nonlinear set-valued quasivariational inclusions involving generalized -accretive mappings in Banach spaces are studied, which included
many variational inclusions studied by others in recent years. By using the properties of the resolvent operator associated with generalized -accretive mappings, we established the equivalence between the generalized nonlinear set-valued quasi-variational inclusions and the fixed point problems, and some new perturbed iterative algorithms, proved that its proximate solution converges strongly to its exact solution in real Banach spaces.