Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 59836, 12 pages
doi:10.1155/JIA/2006/59836
On multivalued nonlinear variational inclusion problems with (A,η)-accretive mappings in Banach spaces
Department of Mathematics, Sichuan University of Science & Engineering, Zigong 643000, Sichuan, China
Received 20 January 2006; Revised 12 May 2006; Accepted 15 May 2006
Copyright © 2006 Heng-You Lan. 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.
Abstract
Based on the notion of (A,η)-accretive mappings and the resolvent operators associated with (A,η)-accretive mappings due to Lan et al., we study a new class of multivalued nonlinear variational inclusion problems with (A,η)-accretive mappings in Banach spaces and construct some new iterative algorithms to approximate the solutions of the nonlinear variational inclusion problems involving (A,η)-accretive mappings. We also prove the existence of solutions and the convergence of the sequences generated by the algorithms in q-uniformly smooth Banach spaces.